[586] | 1 | #define BDMLIB |
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[717] | 2 | #include "../mat_checks.h" |
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[1130] | 3 | #include "design/lq_ctrl.h" |
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[586] | 4 | |
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| 5 | using namespace bdm; |
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| 6 | |
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[737] | 7 | TEST ( LQG_test ) { |
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[1064] | 8 | LQG reg; |
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| 9 | shared_ptr<StateSpace<chmat> > stsp = new StateSpace<chmat>; |
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| 10 | // 2 x 1 x 1 |
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| 11 | stsp-> set_parameters ( eye ( 2 ), ones ( 2, 1 ), ones ( 1, 2 ), ones ( 1, 1 ), /* Q,R */ eye ( 2 ), eye ( 1 ) ); |
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| 12 | reg.set_system ( stsp ); // A, B, C |
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| 13 | reg.set_control_parameters ( eye ( 1 ), eye ( 1 ), vec_1 ( 1.0 ), 6 ); //Qy, Qu, horizon |
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| 14 | reg.validate(); |
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[586] | 15 | |
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[1064] | 16 | reg.redesign(); |
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| 17 | double reg_apply = reg.ctrlaction ( "0.5, 1.1", "0.0" ) ( 0 ); /*convert vec to double*/ |
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| 18 | CHECK_CLOSE ( reg_apply, -0.248528137234392, 0.0001 ); |
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[586] | 19 | } |
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| 20 | |
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[737] | 21 | TEST ( to_state_test ) { |
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[1064] | 22 | mlnorm<fsqmat> ml; |
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| 23 | mat A = "1.1, 2.3"; |
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| 24 | ml.set_parameters ( A, vec_1 ( 1.3 ), eye ( 1 ) ); |
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| 25 | RV yr = RV ( "y", 1 ); |
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| 26 | RV ur = RV ( "u", 1 ); |
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| 27 | ml.set_rv ( yr ); |
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| 28 | yr.t_plus ( -1 ); |
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| 29 | ml.set_rvc ( concat ( yr, ur ) ); |
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[737] | 30 | |
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[1064] | 31 | shared_ptr<StateCanonical > Stsp = new StateCanonical; |
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| 32 | Stsp->connect_mlnorm ( ml ); |
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[737] | 33 | |
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[1064] | 34 | /* results from |
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| 35 | [A,B,C,D]=tf2ss([2.3 0],[1 -1.1]) |
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| 36 | */ |
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| 37 | CHECK_CLOSE_EX ( Stsp->_A().get_row ( 0 ), vec ( "1.1" ), 0.0001 ); |
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| 38 | CHECK_CLOSE_EX ( Stsp->_C().get_row ( 0 ), vec ( "2.53" ), 0.0001 ); |
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| 39 | CHECK_CLOSE_EX ( Stsp->_D().get_row ( 0 ), vec ( "2.30" ), 0.0001 ); |
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[605] | 40 | } |
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| 41 | |
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[737] | 42 | TEST ( to_state_arx_test ) { |
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[1064] | 43 | mlnorm<chmat> ml; |
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| 44 | mat A = "1.1, 2.3, 3.4"; |
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| 45 | ml.set_parameters ( A, vec_1 ( 1.3 ), eye ( 1 ) ); |
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| 46 | RV yr = RV ( "y", 1 ); |
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| 47 | RV ur = RV ( "u", 1 ); |
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| 48 | ml.set_rv ( yr ); |
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| 49 | ml.set_rvc ( concat ( yr.copy_t ( -1 ), concat ( ur, ur.copy_t ( -1 ) ) ) ); |
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[737] | 50 | |
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[1064] | 51 | shared_ptr<StateFromARX> Stsp = new StateFromARX; |
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| 52 | RV xrv; |
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| 53 | RV urv; |
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| 54 | Stsp->connect_mlnorm ( ml, xrv, urv ); |
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[737] | 55 | |
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[1064] | 56 | /* results from |
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| 57 | [A,B,C,D]=tf2ss([2.3 0],[1 -1.1]) |
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| 58 | */ |
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| 59 | CHECK_CLOSE_EX ( Stsp->_A().get_row ( 0 ), vec ( "1.1, 3.4, 1.3" ), 0.0001 ); |
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| 60 | CHECK_CLOSE_EX ( Stsp->_B().get_row ( 0 ), vec ( "2.3" ), 0.0001 ); |
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| 61 | CHECK_CLOSE_EX ( Stsp->_C().get_row ( 0 ), vec ( "1, 0, 0" ), 0.0001 ); |
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[703] | 62 | } |
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| 63 | |
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[737] | 64 | TEST ( arx_LQG_test ) { |
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[1064] | 65 | mlnorm<chmat> ml; |
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| 66 | mat A = "1.81, -.81, .00468, .00438"; |
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| 67 | ml.set_parameters ( A, vec_1 ( 0.0 ), 0.00001*eye ( 1 ) ); |
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| 68 | RV yr = RV ( "y", 1 ); |
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| 69 | RV ur = RV ( "u", 1 ); |
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| 70 | RV rgr = yr.copy_t ( -1 ); |
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| 71 | rgr.add ( yr.copy_t ( -2 ) ); |
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| 72 | rgr.add ( yr.copy_t ( -2 ) ); |
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| 73 | rgr.add ( ur.copy_t ( -1 ) ); |
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| 74 | rgr.add ( ur ); |
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[737] | 75 | |
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[1064] | 76 | ml.set_rv ( yr ); |
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| 77 | ml.set_rvc ( rgr ); |
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| 78 | ml.validate(); |
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[737] | 79 | |
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[1064] | 80 | shared_ptr<StateFromARX> Stsp = new StateFromARX; |
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| 81 | RV xrv; |
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| 82 | RV urv; |
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| 83 | Stsp->connect_mlnorm ( ml, xrv, urv ); |
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[737] | 84 | |
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[1064] | 85 | LQG L; |
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| 86 | L.set_system ( Stsp ); |
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| 87 | L.set_control_parameters ( eye ( 1 ), sqrt ( 1.0 / 1000 ) *eye ( 1 ), vec_1 ( 0.0 ), 100 ); |
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| 88 | L.validate(); |
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[737] | 89 | |
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[1064] | 90 | L.redesign(); |
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| 91 | cout << L.to_string() << endl; |
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[699] | 92 | } |
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[1130] | 93 | |
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| 94 | TEST (quadratic_test){ |
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[1157] | 95 | /*quadraticfn qf; |
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[1130] | 96 | qf.Q = chmat(2); |
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| 97 | qf.Q._Ch() = mat("1 -1 0; 0 0 0; 0 0 0"); |
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| 98 | CHECK_CLOSE_EX(qf.eval(vec("1 2")), vec_1(1.0), 0.0000000000000001); |
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| 99 | |
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| 100 | LQG_universal lq; |
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| 101 | lq.Losses = Array<quadraticfn>(1); |
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| 102 | lq.Losses(0) = quadraticfn(); |
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| 103 | lq.Losses(0).Q._Ch() = mat("1 -1 0; 0 0 0; 0 0 0"); |
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| 104 | lq.Losses(0).rv = RV("{u up }"); |
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| 105 | |
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[1157] | 106 | lq.Models = Array<linfnEx>(1); |
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| 107 | lq.Models(0) = linfnEx(mat("1"),vec("1")); |
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[1130] | 108 | lq.Models(0).rv = RV("{x }"); |
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| 109 | |
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| 110 | lq.rv = RV("u",1); |
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| 111 | |
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| 112 | lq.redesign(); |
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[1157] | 113 | CHECK_CLOSE_EX(lq.ctrlaction(vec("1,0")), vec("1.24, -5.6"), 0.0000001);*/ |
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| 114 | } |
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| 115 | |
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[1194] | 116 | TEST (LQGU_static_vs_Riccati_test){ |
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[1157] | 117 | //test of universal LQG controller |
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| 118 | LQG_universal lq; |
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| 119 | lq.rv = RV("u", 2, 0); |
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| 120 | lq.set_rvc(RV("x", 2, 0)); |
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| 121 | lq.horizon = 10; |
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| 122 | |
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| 123 | /* |
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| 124 | model: x = Ax + Bu time: 0..horizon |
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| 125 | loss: l = x'Q'Qx + u'R'Ru time: 0..horizon-1 |
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| 126 | final loss: l = x'S'Sx time: horizon |
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| 127 | |
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| 128 | dim: x: 2 |
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| 129 | u: 2 |
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| 130 | |
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| 131 | A = [ 2 -1 ] |
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| 132 | [ 0 0.5 ] |
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| 133 | |
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| 134 | B = [ 1 -0.1 ] |
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| 135 | [ -0.2 2 ] |
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| 136 | |
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| 137 | Q = [ 5 0 ] |
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| 138 | [ 0 1 ] |
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| 139 | |
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| 140 | R = [ 0.01 0 ] |
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| 141 | [ 0 0.1 ] |
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| 142 | |
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| 143 | S = Q |
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| 144 | */ |
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| 145 | |
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[1194] | 146 | mat mA("2 -1;0 0.5"); |
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| 147 | mat mB("1 -0.1;-0.2 2"); |
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| 148 | mat mQ("5 0;0 1"); |
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| 149 | mat mR("0.01 0;0 0.1"); |
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| 150 | mat mS = mQ; |
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[1157] | 151 | |
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| 152 | //starting configuration |
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[1194] | 153 | vec x0("6 3"); |
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[1157] | 154 | |
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| 155 | /*cout << "configuration:" << endl |
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| 156 | << "mA:" << endl << mA << endl |
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| 157 | << "mB:" << endl << mB << endl |
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| 158 | << "mQ:" << endl << mQ << endl |
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| 159 | << "mR:" << endl << mR << endl |
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| 160 | << "mS:" << endl << mS << endl |
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| 161 | << "x0:" << endl << x0 << endl;*/ |
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| 162 | |
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| 163 | //model |
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| 164 | Array<linfnEx> model(2); |
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| 165 | //model Ax part |
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| 166 | model(0).A = mA; |
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| 167 | model(0).B = vec("0 0"); |
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| 168 | model(0).rv = RV("x", 2, 0); |
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| 169 | model(0).rv_ret = RV("x", 2, 1); |
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| 170 | //model Bu part |
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| 171 | model(1).A = mB; |
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| 172 | model(1).B = vec("0 0"); |
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| 173 | model(1).rv = RV("u", 2, 0); |
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| 174 | model(1).rv_ret = RV("x", 2, 1); |
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| 175 | //setup |
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| 176 | lq.Models = model; |
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| 177 | |
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| 178 | //loss |
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| 179 | Array<quadraticfn> loss(2); |
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| 180 | //loss x'Qx part |
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| 181 | loss(0).Q.setCh(mQ); |
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| 182 | loss(0).rv = RV("x", 2, 0); |
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| 183 | //loss u'Ru part |
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| 184 | loss(1).Q.setCh(mR); |
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| 185 | loss(1).rv = RV("u", 2, 0); |
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| 186 | //setup |
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| 187 | lq.Losses = loss; |
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| 188 | |
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| 189 | //finalloss setup |
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| 190 | lq.finalLoss.Q.setCh(mS); |
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| 191 | lq.finalLoss.rv = RV("x", 2, 1); |
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[1194] | 192 | |
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| 193 | lq.validate(); |
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[1157] | 194 | |
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| 195 | //default L |
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| 196 | //cout << "default L matrix:" << endl << lq.getL() << endl; |
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| 197 | |
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| 198 | //produce last control matrix L |
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| 199 | lq.redesign(); |
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| 200 | |
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| 201 | //verification via Riccati LQG version |
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| 202 | mat mK = mS; |
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| 203 | mat mL = - inv(mR + mB.transpose() * mK * mB) * mB.transpose() * mK * mA; |
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| 204 | |
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| 205 | //cout << "L matrix LQG_universal:" << endl << lq.getL() << endl << |
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| 206 | //"L matrix LQG Riccati:" << endl << mL << endl; |
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| 207 | |
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| 208 | //checking L matrix (universal vs Riccati), tolerance is high, but L is not main criterion |
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| 209 | //more important is reached loss compared in the next part |
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| 210 | double tolerr = 1;//0.01; //0.01 OK x 0.001 NO OK |
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| 211 | |
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| 212 | //check last time L matrix |
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| 213 | CHECK_CLOSE_EX(lq.getL().get_cols(0,1), mL, tolerr); |
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| 214 | |
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| 215 | mat oldK; |
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| 216 | int i; |
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| 217 | |
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| 218 | //produce next control matrix L |
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| 219 | for(i = 0; i < lq.horizon - 1; i++) { |
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| 220 | lq.redesign(); |
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| 221 | oldK = mK; |
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| 222 | mK = mA.transpose() * (oldK - oldK * mB * inv(mR + mB.transpose() * oldK * mB) * mB.transpose() * oldK) * mA + mQ; |
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| 223 | mL = - inv(mR + mB.transpose() * mK * mB) * mB.transpose() * mK * mA; |
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| 224 | |
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| 225 | //cout << "L matrix LQG_universal:" << endl << lq.getL() << endl << |
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| 226 | //"L matrix LQG Riccati:" << endl << mL << endl; |
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| 227 | |
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| 228 | //check other times L matrix |
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| 229 | CHECK_CLOSE_EX(lq.getL().get_cols(0,1), mL, tolerr); |
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| 230 | } |
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| 231 | |
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| 232 | //check losses of LQG control - compare LQG_universal and Riccati version, no noise |
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| 233 | |
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| 234 | //loss of LQG_universal |
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| 235 | /*double*/vec loss_uni("0"); |
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| 236 | |
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| 237 | //setup |
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| 238 | vec x = x0; |
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| 239 | vec xold = x; |
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| 240 | vec u; |
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| 241 | //vec tmploss; |
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| 242 | |
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| 243 | //iteration |
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| 244 | for(i = 0; i < lq.horizon - 1; i++){ |
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| 245 | u = lq.getL().get_cols(0,1) * xold; |
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| 246 | x = mA * xold + mB * u; |
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| 247 | /*tmploss*/loss_uni = x.transpose() * mQ * x + u.transpose() * mR * u; |
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| 248 | //loss_uni += tmploss.get(0); |
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| 249 | xold = x; |
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| 250 | } |
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| 251 | /*tmploss*/ loss_uni = x.transpose() * mS * x; |
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| 252 | //loss_uni += tmploss.get(0); |
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| 253 | |
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| 254 | //loss of LQG Riccati version |
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| 255 | /*double*/ vec loss_rct("0"); |
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| 256 | |
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| 257 | //setup |
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| 258 | x = x0; |
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| 259 | xold = x; |
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| 260 | |
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| 261 | //iteration |
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| 262 | for(i = 0; i < lq.horizon - 1; i++){ |
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| 263 | u = mL * xold; |
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| 264 | x = mA * xold + mB * u; |
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| 265 | /*tmploss*/loss_rct = x.transpose() * mQ * x + u.transpose() * mR * u; |
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| 266 | //loss_rct += tmploss.get(0); |
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| 267 | xold = x; |
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| 268 | } |
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| 269 | /*tmploss*/loss_rct = x.transpose() * mS * x; |
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| 270 | //loss_rct += tmploss.get(0); |
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| 271 | |
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| 272 | //cout << "Loss LQG_universal: " << loss_uni << " vs Loss LQG Riccati: " << loss_rct << endl; |
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[1194] | 273 | CHECK_CLOSE_EX(loss_uni, loss_rct, 0.0001); |
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| 274 | } |
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| 275 | |
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| 276 | TEST (LQGU_random_vs_Riccati_test){ |
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| 277 | |
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| 278 | //uniform random generator |
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| 279 | Uniform_RNG urng; |
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| 280 | double maxmult = 10.0; |
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| 281 | int maxxsize = 5; |
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| 282 | int maxusize = 5; |
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| 283 | |
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| 284 | urng.setup(2.0, maxxsize); |
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| 285 | int matxsize = round(urng()); |
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| 286 | urng.setup(2.0, maxusize); |
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| 287 | int matusize = round(urng()); |
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| 288 | |
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| 289 | urng.setup(-maxmult, maxmult); |
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| 290 | |
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| 291 | mat tmpmat; |
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| 292 | |
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| 293 | mat mA; |
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| 294 | mA = urng(matxsize, matxsize); |
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| 295 | mat mB; |
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| 296 | mB = urng(matxsize, matusize); |
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| 297 | mat mQ; |
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| 298 | tmpmat = urng(matxsize, matxsize); |
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| 299 | mQ = tmpmat*tmpmat.transpose(); |
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| 300 | mat mR; |
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| 301 | tmpmat = urng(matusize, matusize); |
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| 302 | mR = tmpmat*tmpmat.transpose(); |
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| 303 | mat mS; |
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| 304 | tmpmat = urng(matxsize, matxsize); |
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| 305 | mS = tmpmat*tmpmat.transpose(); |
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| 306 | |
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| 307 | //starting configuration |
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| 308 | vec x0; |
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| 309 | x0 = urng(matxsize); |
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| 310 | |
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| 311 | /*cout << "configuration:" << endl |
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| 312 | << "x size " << matxsize << " u size " << matusize << endl |
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| 313 | << "mA:" << endl << mA << endl |
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| 314 | << "mB:" << endl << mB << endl |
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| 315 | << "mQ:" << endl << mQ << endl |
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| 316 | << "mR:" << endl << mR << endl |
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| 317 | << "mS:" << endl << mS << endl |
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| 318 | << "x0:" << endl << x0 << endl;*/ |
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| 319 | |
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| 320 | vec zerovecx(matxsize); |
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| 321 | zerovecx.zeros(); |
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| 322 | vec zerovecu(matusize); |
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| 323 | zerovecu.zeros(); |
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| 324 | |
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| 325 | //test of universal LQG controller |
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| 326 | LQG_universal lq; |
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| 327 | lq.rv = RV("u", matusize, 0); |
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| 328 | lq.set_rvc(RV("x", matxsize, 0)); |
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| 329 | lq.horizon = 10; |
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| 330 | |
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| 331 | //model |
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| 332 | Array<linfnEx> model(2); |
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| 333 | //model Ax part |
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| 334 | model(0).A = mA; |
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| 335 | model(0).B = zerovecx; |
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| 336 | model(0).rv = RV("x", matxsize, 0); |
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| 337 | model(0).rv_ret = RV("x", matxsize, 1); |
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| 338 | //model Bu part |
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| 339 | model(1).A = mB; |
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| 340 | model(1).B = zerovecu; |
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| 341 | model(1).rv = RV("u", matusize, 0); |
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| 342 | model(1).rv_ret = RV("x", matxsize, 1); |
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| 343 | //setup |
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| 344 | lq.Models = model; |
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| 345 | |
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| 346 | //loss |
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| 347 | Array<quadraticfn> loss(2); |
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| 348 | //loss x'Qx part |
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| 349 | loss(0).Q.setCh(mQ); |
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| 350 | loss(0).rv = RV("x", matxsize, 0); |
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| 351 | //loss u'Ru part |
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| 352 | loss(1).Q.setCh(mR); |
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| 353 | loss(1).rv = RV("u", matusize, 0); |
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| 354 | //setup |
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| 355 | lq.Losses = loss; |
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| 356 | |
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| 357 | //finalloss setup |
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| 358 | lq.finalLoss.Q.setCh(mS); |
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| 359 | lq.finalLoss.rv = RV("x", matxsize, 1); |
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| 360 | |
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| 361 | lq.validate(); |
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| 362 | |
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| 363 | //produce last control matrix L |
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| 364 | lq.redesign(); |
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| 365 | |
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| 366 | //verification via Riccati LQG version |
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| 367 | mat mK = mS; |
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| 368 | mat mL = - inv(mR + mB.transpose() * mK * mB) * mB.transpose() * mK * mA; |
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| 369 | |
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| 370 | //checking L matrix (universal vs Riccati), tolerance is high, but L is not main criterion |
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| 371 | //more important is reached loss compared in the next part |
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| 372 | double tolerr = 2;//1;//0.01; //0.01 OK x 0.001 NO OK |
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| 373 | |
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| 374 | //check last time L matrix |
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| 375 | CHECK_CLOSE_EX(lq.getL().get_cols(0,(matxsize-1)), mL, tolerr); |
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| 376 | |
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| 377 | mat oldK; |
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| 378 | int i; |
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| 379 | |
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| 380 | //produce next control matrix L |
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| 381 | for(i = 0; i < lq.horizon - 1; i++) { |
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| 382 | lq.redesign(); |
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| 383 | oldK = mK; |
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| 384 | mK = mA.transpose() * (oldK - oldK * mB * inv(mR + mB.transpose() * oldK * mB) * mB.transpose() * oldK) * mA + mQ; |
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| 385 | mL = - inv(mR + mB.transpose() * mK * mB) * mB.transpose() * mK * mA; |
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| 386 | |
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| 387 | //check other times L matrix |
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| 388 | CHECK_CLOSE_EX(lq.getL().get_cols(0,(matxsize-1)), mL, tolerr); |
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| 389 | } |
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| 390 | |
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| 391 | //check losses of LQG control - compare LQG_universal and Riccati version, no noise |
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| 392 | |
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| 393 | //loss of LQG_universal |
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| 394 | vec loss_uni("0"); |
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| 395 | |
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| 396 | //setup |
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| 397 | vec x = x0; |
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| 398 | vec xold = x; |
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| 399 | vec u; |
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| 400 | //vec tmploss; |
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| 401 | |
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| 402 | //iteration |
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| 403 | for(i = 0; i < lq.horizon - 1; i++){ |
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| 404 | u = lq.getL().get_cols(0,(matxsize-1)) * xold; |
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| 405 | x = mA * xold + mB * u; |
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| 406 | loss_uni = x.transpose() * mQ * x + u.transpose() * mR * u; |
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| 407 | xold = x; |
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| 408 | } |
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| 409 | |
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| 410 | loss_uni = x.transpose() * mS * x; |
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| 411 | |
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| 412 | //loss of LQG Riccati version |
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| 413 | vec loss_rct("0"); |
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| 414 | |
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| 415 | //setup |
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| 416 | x = x0; |
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| 417 | xold = x; |
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| 418 | |
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| 419 | //iteration |
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| 420 | for(i = 0; i < lq.horizon - 1; i++){ |
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| 421 | u = mL * xold; |
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| 422 | x = mA * xold + mB * u; |
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| 423 | loss_rct = x.transpose() * mQ * x + u.transpose() * mR * u; |
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| 424 | xold = x; |
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| 425 | } |
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| 426 | loss_rct = x.transpose() * mS * x; |
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| 427 | |
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| 428 | CHECK_CLOSE_EX(loss_uni, loss_rct, 0.0001); |
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| 429 | } |
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| 430 | |
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| 431 | TEST (LQGU_SiSy_test){ |
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| 432 | int K = 5; |
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| 433 | int N = 100; |
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| 434 | double sigma = 0.1; |
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| 435 | double yr = 1; |
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| 436 | double y0 = 0; |
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| 437 | double x0 = y0 - yr; |
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| 438 | double Eb = 1; |
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| 439 | double P; |
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| 440 | //double P = 0.01; //loss ~ 1.0??? e-2 |
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| 441 | //double P = 0.1; //loss ~ 1.??? e-1 |
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| 442 | //double P = 1; //loss ~ ???.??? e+2 |
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| 443 | //double P = 10; //loss ~ ?e+6 |
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| 444 | |
---|
| 445 | mat A("1"); |
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| 446 | mat B(1,1); |
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| 447 | B(0,0) = Eb; |
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| 448 | mat Q("1"); |
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| 449 | mat R("0"); |
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| 450 | |
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| 451 | vec u(K); |
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| 452 | u.zeros(); |
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| 453 | mat xn(K, N); |
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| 454 | xn.zeros(); |
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| 455 | vec S(K); |
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| 456 | S.zeros(); |
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| 457 | vec L(K); |
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| 458 | L.zeros(); |
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| 459 | |
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| 460 | vec loss(N); |
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| 461 | loss.zeros(); |
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| 462 | |
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| 463 | LQG_universal lq; |
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| 464 | lq.rv = RV("u", 1, 0); |
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| 465 | lq.set_rvc(RV("x", 1, 0)); |
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| 466 | lq.horizon = K; |
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| 467 | |
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| 468 | Array<linfnEx> model(2); |
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| 469 | model(0).A = A; |
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| 470 | model(0).B = vec("0 0"); |
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| 471 | model(0).rv = RV("x", 1, 0); |
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| 472 | model(0).rv_ret = RV("x", 1, 1); |
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| 473 | model(1).A = B; |
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| 474 | model(1).B = vec("0 0"); |
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| 475 | model(1).rv = RV("u", 1, 0); |
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| 476 | model(1).rv_ret = RV("x", 1, 1); |
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| 477 | lq.Models = model; |
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| 478 | |
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| 479 | Array<quadraticfn> qloss(2); |
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| 480 | qloss(0).Q.setCh(Q); |
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| 481 | qloss(0).rv = RV("x", 1, 0); |
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| 482 | qloss(1).Q.setCh(R); |
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| 483 | qloss(1).rv = RV("u", 1, 0); |
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| 484 | lq.Losses = qloss; |
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| 485 | |
---|
| 486 | lq.finalLoss.Q.setCh(Q); |
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| 487 | lq.finalLoss.rv = RV("x", 1, 1); |
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| 488 | |
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| 489 | lq.validate(); |
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| 490 | |
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| 491 | int n, k; |
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| 492 | double Br; |
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| 493 | //double x00; |
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| 494 | |
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| 495 | for(k = K-1; k >= 0;k--){ |
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| 496 | lq.redesign(); |
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| 497 | L(k) = (lq.getL())(0,0); |
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| 498 | } |
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| 499 | |
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| 500 | for(P = 0.01; P <= 10; (P*=10)){ |
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| 501 | lq.resetTime(); |
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| 502 | |
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| 503 | //cout << "Ls " << L << endl; |
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| 504 | for(n = 0; n < N; n++){ |
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| 505 | Br = Eb + sqrt(P)*randn(); |
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| 506 | |
---|
| 507 | xn(0, n) = x0 + sigma*randn(); |
---|
| 508 | for(k = 0; k < K-1; k++){ |
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| 509 | u(k) = L(k)*xn(k, n); |
---|
| 510 | xn(k+1, n) = (A*xn(k, n))(0,0) + Br*u(k) + sigma*randn(); |
---|
| 511 | } |
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| 512 | |
---|
| 513 | loss(n) = 0; |
---|
| 514 | for(k=0;k<K;k++) loss(n) += xn(k, n)*xn(k, n); |
---|
| 515 | |
---|
| 516 | } |
---|
| 517 | |
---|
| 518 | /*vec mtraj(K); |
---|
| 519 | for(k=0;k<K;k++){ |
---|
| 520 | mtraj(k) = 0; |
---|
| 521 | for(n = 0; n < N; n++) mtraj(k) += xn(k, n); |
---|
| 522 | mtraj(k) /= N; |
---|
| 523 | mtraj(k) += yr; |
---|
| 524 | } |
---|
| 525 | cout << "prum trajek " << mtraj << endl;*/ |
---|
| 526 | //cout << "prum ztrata " << sum(loss)/N << endl; |
---|
| 527 | //rfloss = mean(loss); |
---|
| 528 | //rftraj = (mean((xn(1:K, :)), 2) + yr*ones(K, 1))'; |
---|
| 529 | |
---|
| 530 | double tolerr; |
---|
| 531 | //double P = 0.01; //loss ~ 1.0??? e-2 |
---|
| 532 | //double P = 0.1; //loss ~ 1.??? e-1 |
---|
| 533 | //double P = 1; //loss ~ ???.??? e+2 |
---|
| 534 | //double P = 10; //loss ~ ?e+6 |
---|
| 535 | if(P == 0.01) tolerr = 0.2; |
---|
| 536 | else if(P == 0.1) tolerr = 2; |
---|
| 537 | else if(P == 1) tolerr = 2000; |
---|
| 538 | else if(P == 10) tolerr = 2e+7; |
---|
| 539 | else tolerr = 0; |
---|
| 540 | |
---|
| 541 | CHECK_CLOSE_EX(1.0, sum(loss)/N, tolerr); |
---|
| 542 | } |
---|
| 543 | } |
---|
| 544 | |
---|
| 545 | TEST (LQGU_SiSy_SuSt_test){ |
---|
| 546 | int K = 5; |
---|
| 547 | int N = 100; |
---|
| 548 | double sigma = 0.1; |
---|
| 549 | double yr = 1; |
---|
| 550 | double y0 = 0; |
---|
| 551 | double Eb = 1; |
---|
| 552 | double inP; |
---|
| 553 | //double inP = 0.01; //loss ~ 1.0??? e-2 |
---|
| 554 | //double inP = 0.1; //loss ~ 1.0??? e-2 |
---|
| 555 | //double inP = 1; //loss ~ 1.0??? e-2 |
---|
| 556 | //double inP = 10; //loss ~ 1.0??? e-2 |
---|
| 557 | |
---|
| 558 | vec x0(3); |
---|
| 559 | x0(0) = y0 - yr; |
---|
| 560 | x0(1) = Eb; |
---|
| 561 | //x0(2) = inP; |
---|
| 562 | |
---|
| 563 | mat A("1 0 0; 0 1 0; 0 0 1"); |
---|
| 564 | mat B("0; 0; 0"); |
---|
| 565 | mat X("1 0 0; 0 0 0; 0 0 0"); |
---|
| 566 | mat Y("0.00001"); |
---|
| 567 | mat Q(3,3); |
---|
| 568 | Q.zeros(); |
---|
| 569 | Q(1,1) = sigma*sigma; |
---|
| 570 | //mat R("0"); |
---|
| 571 | //mat P(3,3); |
---|
| 572 | // P.zeros(); |
---|
| 573 | |
---|
| 574 | vec u(K); |
---|
| 575 | u.zeros(); |
---|
| 576 | vec Kk(K); |
---|
| 577 | Kk.zeros(); |
---|
| 578 | mat xn0(K+1, N); |
---|
| 579 | xn0.zeros(); |
---|
| 580 | mat xn1(K+1, N); |
---|
| 581 | xn1.zeros(); |
---|
| 582 | mat xn2(K+1, N); |
---|
| 583 | xn2.zeros(); |
---|
| 584 | //vec S(K); |
---|
| 585 | // S.zeros(); |
---|
| 586 | //vec L(K); |
---|
| 587 | // L.zeros(); |
---|
| 588 | mat L(1, 3); |
---|
| 589 | L.zeros(); |
---|
| 590 | vec loss(N); |
---|
| 591 | loss.zeros(); |
---|
| 592 | |
---|
| 593 | LQG_universal lq; |
---|
| 594 | lq.rv = RV("u", 1, 0); |
---|
| 595 | lq.set_rvc(RV("x", 3, 0)); |
---|
| 596 | lq.horizon = K; |
---|
| 597 | |
---|
| 598 | Array<linfnEx> model(2); |
---|
| 599 | model(0).A = A; |
---|
| 600 | model(0).B = vec("0 0"); |
---|
| 601 | model(0).rv = RV("x", 3, 0); |
---|
| 602 | model(0).rv_ret = RV("x", 3, 1); |
---|
| 603 | model(1).A = B; |
---|
| 604 | model(1).B = vec("0 0"); |
---|
| 605 | model(1).rv = RV("u", 1, 0); |
---|
| 606 | model(1).rv_ret = RV("x", 3, 1); |
---|
| 607 | lq.Models = model; |
---|
| 608 | |
---|
| 609 | Array<quadraticfn> qloss(2); |
---|
| 610 | qloss(0).Q.setCh(X); |
---|
| 611 | qloss(0).rv = RV("x", 3, 0); |
---|
| 612 | qloss(1).Q.setCh(Y); |
---|
| 613 | qloss(1).rv = RV("u", 1, 0); |
---|
| 614 | lq.Losses = qloss; |
---|
| 615 | |
---|
| 616 | lq.finalLoss.Q.setCh(X); |
---|
| 617 | lq.finalLoss.rv = RV("x", 3, 1); |
---|
| 618 | |
---|
| 619 | lq.validate(); |
---|
| 620 | |
---|
| 621 | int n, k; |
---|
| 622 | //double Br; |
---|
| 623 | //double x00; |
---|
| 624 | |
---|
| 625 | /*for(k = K-1; k >= 0;k--){ |
---|
| 626 | lq.redesign(); |
---|
| 627 | L(k) = (lq.getL())(0,0); |
---|
| 628 | }*/ |
---|
| 629 | //cout << "Ls " << L << endl; |
---|
| 630 | for(inP = 0.01; inP <= 10; (inP*=10)){ |
---|
| 631 | lq.resetTime(); |
---|
| 632 | x0(2) = inP; |
---|
| 633 | for(n = 0; n < N; n++){ |
---|
| 634 | L.zeros(); |
---|
| 635 | xn0(0, n) = x0(0); |
---|
| 636 | xn1(0, n) = x0(1) + sqrt(inP) * randn(); |
---|
| 637 | xn2(0, n) = x0(2); |
---|
| 638 | //^neznalost, sum zatim ne |
---|
| 639 | |
---|
| 640 | for(k = 0; k < K-1; k++){ |
---|
| 641 | u(k) = L(0)*xn0(k, n) + L(1)*xn1(k, n) + L(2)*xn2(k, n); |
---|
| 642 | Kk(k) = u(k)*xn2(k, n)/(u(k)*u(k)*xn2(k, n) + sigma*sigma); |
---|
| 643 | xn0(k+1, n) = xn0(k, n) + xn1(k, n)*u(k) + sigma*randn(); |
---|
| 644 | xn1(k+1, n) = xn1(k, n) + Kk(k)*(xn0(k+1, n) - xn0(k, n) - xn1(k, n)*u(k)); |
---|
| 645 | xn2(k+1, n) = (1 - Kk(k)*u(k))*xn2(k, n); |
---|
| 646 | } |
---|
| 647 | |
---|
| 648 | lq.resetTime(); |
---|
| 649 | lq.redesign(); |
---|
| 650 | for(k = K-1; k > 0; k--){ |
---|
| 651 | A(0, 1) = u(k); |
---|
| 652 | A(1, 0) = -Kk(k); |
---|
| 653 | A(1, 1) = 1-Kk(k)*u(k); |
---|
| 654 | A(1, 2) = u(k)*sigma*sigma*(xn0(k+1, n) - xn0(k, n) - xn1(k, n)*u(k)) / sqr(u(k)*u(k)*xn2(k, n) + sigma*sigma); |
---|
| 655 | A(2, 2) = 1 - u(k)*u(k)*xn2(k, n)*(u(k)*u(k)*xn2(k, n) + 2*sigma*sigma) / sqr(u(k)*u(k)*xn2(k, n) + sigma*sigma); |
---|
| 656 | B(0) = xn1(k, n); |
---|
| 657 | B(1) = ((xn2(k, n)*sigma*sigma-u(k)*u(k)*xn2(k, n)*xn2(k, n))*(xn0(k+1, n)-xn0(k, n)) - 2*xn1(k, n)*u(k)) / sqr(u(k)*u(k)*xn2(k, n) + sigma*sigma); |
---|
| 658 | B(2) = -2*u(k)*xn2(k, n)*xn2(k, n)*sigma*sigma / sqr(u(k)*u(k)*xn2(k, n) + sigma*sigma); |
---|
| 659 | lq.Models(0).A = A; |
---|
| 660 | lq.Models(1).A = B; |
---|
| 661 | lq.redesign(); |
---|
| 662 | } |
---|
| 663 | L = lq.getL(); |
---|
| 664 | |
---|
| 665 | //simulation |
---|
| 666 | xn0(0, n) += sigma*randn(); |
---|
| 667 | for(k = 0; k < K-1; k++){ |
---|
| 668 | u(k) = L(0)*xn0(k, n) + L(1)*xn1(k, n) + L(2)*xn2(k, n); |
---|
| 669 | Kk(k) = u(k)*xn2(k, n)/(u(k)*u(k)*xn2(k, n) + sigma*sigma); |
---|
| 670 | xn0(k+1, n) = xn0(k, n) + xn1(k, n)*u(k) + sigma*randn(); |
---|
| 671 | xn1(k+1, n) = xn1(k, n) + Kk(k)*(xn0(k+1, n) - xn0(k, n) - xn1(k, n)*u(k)); |
---|
| 672 | xn2(k+1, n) = (1 - Kk(k)*u(k))*xn2(k, n); |
---|
| 673 | } |
---|
| 674 | |
---|
| 675 | |
---|
| 676 | loss(n) = 0; |
---|
| 677 | for(k=0;k<K;k++) loss(n) += xn0(k, n)*xn0(k, n); |
---|
| 678 | |
---|
| 679 | } |
---|
| 680 | |
---|
| 681 | /*vec mtraj(K); |
---|
| 682 | for(k=0;k<K;k++){ |
---|
| 683 | mtraj(k) = 0; |
---|
| 684 | for(n = 0; n < N; n++) mtraj(k) += xn0(k, n); |
---|
| 685 | mtraj(k) /= N; |
---|
| 686 | mtraj(k) += yr; |
---|
| 687 | } |
---|
| 688 | cout << "prum trajek " << mtraj << endl;*/ |
---|
| 689 | //cout << "prum ztrata " << sum(loss)/N << endl; |
---|
| 690 | |
---|
| 691 | double tolerr = 0.2; |
---|
| 692 | /*if(inP == 0.01) tolerr = 0.2; |
---|
| 693 | else if(inP == 0.1) tolerr = 2; |
---|
| 694 | else if(inP == 1) tolerr = 2000; |
---|
| 695 | else if(inP == 10) tolerr = 2e+7; |
---|
| 696 | else tolerr = 0;*/ |
---|
| 697 | |
---|
| 698 | CHECK_CLOSE_EX(1.0, sum(loss)/N, tolerr); |
---|
| 699 | } |
---|
| 700 | } |
---|
| 701 | |
---|
| 702 | TEST (LQGU_PMSM_test){ |
---|
| 703 | bdm_assert(0, "Test not implemented."); |
---|
| 704 | } |
---|
| 705 | |
---|
| 706 | TEST (LQGU_large_test){ |
---|
| 707 | bdm_assert(0, "Test not implemented."); |
---|
| 708 | } |
---|
| 709 | |
---|
| 710 | TEST (validation_test){ |
---|
| 711 | RV rv1("x", 1); |
---|
| 712 | RV rv2("y", 2); |
---|
| 713 | RV rv3("z", 3); |
---|
| 714 | RV rv4("u", 2); |
---|
| 715 | RV rv5("v", 1); |
---|
| 716 | RV all; |
---|
| 717 | all = rv1; |
---|
| 718 | all.add(rv2); |
---|
| 719 | all.add(rv3); |
---|
| 720 | all.add(rv4); |
---|
| 721 | all.add(rv5); |
---|
| 722 | all.add(RV("1",1,0)); |
---|
| 723 | cout << "all rv: " << all << endl; |
---|
| 724 | |
---|
| 725 | ivec fy = rv2.findself(all); |
---|
| 726 | cout << "finding y: " << fy << endl; |
---|
| 727 | ivec dy = rv2.dataind(all); |
---|
| 728 | cout << "dataind y: " << dy << endl; |
---|
| 729 | |
---|
| 730 | RV rvzyu; |
---|
| 731 | rvzyu = rv3; |
---|
| 732 | rvzyu.add(rv2); |
---|
| 733 | rvzyu.add(rv4); |
---|
| 734 | fy = rvzyu.findself(all); |
---|
| 735 | cout << "finding zyu: " << fy << endl; |
---|
| 736 | dy = rvzyu.dataind(all); |
---|
| 737 | cout << "dataind zyu: " << dy << endl; |
---|
| 738 | |
---|
| 739 | rvzyu.add(RV("1",1,0)); |
---|
| 740 | fy = rvzyu.findself(all); |
---|
| 741 | cout << "finding zyu1: " << fy << endl; |
---|
| 742 | dy = rvzyu.dataind(all); |
---|
| 743 | cout << "dataind zyu1: " << dy << endl; |
---|
| 744 | |
---|
| 745 | rvzyu.add(RV("k",1,0)); |
---|
| 746 | fy = rvzyu.findself(all); |
---|
| 747 | cout << "finding zyu1 !k!: " << fy << endl; |
---|
| 748 | dy = rvzyu.dataind(all); |
---|
| 749 | cout << "dataind zyu1 !k!: " << dy << endl; |
---|
| 750 | |
---|
| 751 | RV emptyrv; |
---|
| 752 | fy = emptyrv.findself(all); |
---|
| 753 | cout << "finding empty: " << fy << " size " << fy.size() << endl; |
---|
| 754 | dy = emptyrv.dataind(all); |
---|
| 755 | cout << "dataind empty: " << dy << " size " << dy.size() << endl; |
---|
| 756 | |
---|
| 757 | LQG_universal lq; |
---|
| 758 | lq.validate(); |
---|
[1130] | 759 | } |
---|