[1420] | 1 | |
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| 2 | #ifndef QUADRATICMINIMALIZATOR_H |
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| 3 | #define QUADRATICMINIMALIZATOR_H |
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| 4 | |
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| 5 | #include <cstdlib> |
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| 6 | #include <itpp/itbase.h> |
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| 7 | #include <iostream> |
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| 8 | |
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| 9 | |
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| 10 | using namespace itpp; |
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| 11 | using namespace std; |
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| 12 | |
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| 13 | class QuadraticMinimalizator { |
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| 14 | protected: |
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| 15 | mat A; |
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| 16 | mat B; |
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| 17 | mat Q; |
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| 18 | mat R; |
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| 19 | double maxdif; |
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| 20 | |
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| 21 | bool test() { |
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| 22 | if ( !isDiagonal(Q) ) { |
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| 23 | stringstream e; |
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| 24 | e << "Matrix Q is not diagonal" << endl; |
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| 25 | e << Q << endl; |
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| 26 | it_warning(e.str()); |
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| 27 | } |
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| 28 | if ( !isDiagonal(R) ) { |
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| 29 | stringstream e; |
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| 30 | e << "Matrix R is not diagonal" << endl; |
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| 31 | e << R << endl; |
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| 32 | it_warning(e.str()); |
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| 33 | } |
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| 34 | if ( !isPositiveDefinite(Q) ) { |
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| 35 | stringstream e; |
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| 36 | e << "Matrix Q is not positive definite" << endl; |
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| 37 | e << Q << endl; |
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| 38 | it_warning(e.str()); |
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| 39 | } |
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| 40 | if ( !isPositiveDefinite(R) ) { |
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| 41 | stringstream e; |
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| 42 | e << "Matrix R is not positive definite" << endl; |
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| 43 | e << R << endl; |
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| 44 | it_warning(e.str()); |
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| 45 | } |
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| 46 | } |
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| 47 | |
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| 48 | public: |
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| 49 | QuadraticMinimalizator( const mat &A, const mat &B, const mat &Q, const mat &R ) { |
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| 50 | maxdif = 0.00000001; |
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| 51 | this->A = A; |
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| 52 | this->B = B; |
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| 53 | this->Q = Q; |
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| 54 | this->R = R; |
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| 55 | test(); |
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| 56 | } |
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| 57 | |
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| 58 | |
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| 59 | /** |
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| 60 | * x(t+1) = Ax(t) + Bu(t) + C |
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| 61 | * @param horizont |
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| 62 | * @param C |
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| 63 | * @return L: u(t) = L [ x(t) 1 ] |
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| 64 | */ |
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| 65 | mat L( const int horizont, const mat & C ) { |
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| 66 | it_warning("Nijak se tam C neprojevuje!!!"); |
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| 67 | int xdim = A.cols(); |
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| 68 | int udim = B.cols(); |
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| 69 | mat sqQ = sqrt(Q); |
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| 70 | mat sqR = sqrt(R); |
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| 71 | mat M0, M; |
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| 72 | mat qrQ; |
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| 73 | mat Lall, Lc1, Lc2, Lc3, Lx1, Lx2, Lu, L; |
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| 74 | M0 = concat_vertical( |
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| 75 | concat_vertical( |
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| 76 | concat_horizontal( sqQ * B, concat_horizontal( sqQ * A, zeros(xdim, udim) ) ), |
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| 77 | concat_horizontal( sqR, concat_horizontal( zeros( udim, xdim ), zeros(udim, udim) ) ) |
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| 78 | ), |
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| 79 | concat_horizontal( zeros( xdim, xdim + udim ) , sqQ * C) |
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| 80 | ); |
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| 81 | |
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| 82 | M = M0; |
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| 83 | for (int h = horizont; h >= 0; h --) { |
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| 84 | qr(M, Lall); |
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| 85 | |
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| 86 | Lu = Lall(0, udim-1, 0, udim-1 ); |
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| 87 | Lx1 = Lall(0, udim-1, udim, udim+xdim-1); |
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| 88 | Lc1 = Lall(0, udim-1, udim+xdim, udim+xdim ); |
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| 89 | Lx2 = Lall(udim, udim+xdim-1, udim, udim+xdim-1); |
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| 90 | Lc2 = Lall(udim, udim+xdim-1, udim+xdim, udim+xdim); |
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| 91 | Lc3 = Lall(udim+xdim, udim+xdim+xdim-1, udim+xdim, udim+xdim); |
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| 92 | M = concat_vertical( |
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| 93 | M0, |
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| 94 | concat_vertical( |
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| 95 | concat_horizontal( Lx2 * B, concat_horizontal( Lx2 * A, Lc2 ) ), |
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| 96 | concat_horizontal( zeros(xdim, xdim + udim), Lc3 ) |
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| 97 | ) |
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| 98 | ); |
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| 99 | } |
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| 100 | L = concat_horizontal( - inv(Lu) * Lx1, - inv(Lu) * Lc1); |
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| 101 | return L; |
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| 102 | } |
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| 103 | /** |
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| 104 | * x(t+1) = Ax(t) + Bu(t) |
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| 105 | * @param horizont |
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| 106 | * @param C |
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| 107 | * @return L: u(t) = Lx(t) |
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| 108 | */ |
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| 109 | mat L( const int horizont ) { |
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| 110 | int xdim = A.cols(); |
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| 111 | int udim = B.cols(); |
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| 112 | mat sqQ = sqrt(Q); |
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| 113 | mat sqR = sqrt(R); |
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| 114 | mat M0, M; |
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| 115 | mat qrQ; |
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| 116 | mat Lall, Ls, Lx, Lu, L; |
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| 117 | M0 = concat_vertical( |
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| 118 | concat_horizontal( sqQ * B, sqQ * A ), |
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| 119 | concat_horizontal( sqR, zeros( udim, xdim ) ) |
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| 120 | ); |
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| 121 | M = M0; |
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| 122 | for (int h = horizont; h >= 0; h --) { |
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| 123 | qr(M, Lall); |
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| 124 | Lu = Lall(0, udim-1, 0, udim-1); |
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| 125 | Lx = Lall(udim, udim+xdim-1, udim, udim+xdim-1); |
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| 126 | Ls = Lall(0, udim-1, udim, udim+xdim-1); |
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| 127 | M = concat_vertical( |
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| 128 | M0, |
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| 129 | concat_horizontal(Lx * B, Lx * A ) |
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| 130 | ); |
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| 131 | } |
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| 132 | L = - inv(Lu) * Ls; |
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| 133 | return L; |
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| 134 | } |
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| 135 | |
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| 136 | double maxDif( const mat & M1, const mat & M2 ) { |
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| 137 | return max(max(abs(M1 - M2), 1)); |
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| 138 | } |
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| 139 | |
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| 140 | bool isSymmetric( const mat & M) { |
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| 141 | return isSymmetric(M, maxdif); |
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| 142 | } |
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| 143 | |
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| 144 | bool isSymmetric( const mat & M, double maxdif ) { |
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| 145 | mat D = abs(M - M.transpose()); |
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| 146 | double m = max(max(D, 1)); |
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| 147 | if ( m < maxdif ) |
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| 148 | return true; |
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| 149 | else |
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| 150 | return false; |
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| 151 | } |
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| 152 | |
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| 153 | bool isDiagonal( const mat M ) { |
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| 154 | mat D = abs(M); |
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| 155 | for ( int i = 0; i < M.rows(); i ++ ) { |
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| 156 | for ( int j = 0; j < M.cols(); j ++ ) { |
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| 157 | if ( i != j && D(i,j) > maxdif ) { |
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| 158 | return false; |
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| 159 | } |
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| 160 | } |
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| 161 | } |
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| 162 | return true; |
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| 163 | } |
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| 164 | |
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| 165 | bool isPositiveDefinite( const mat M ) { |
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| 166 | int dim = M.rows(); |
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| 167 | if ( dim != M.cols() ) { |
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| 168 | stringstream err; |
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| 169 | err << "Matrix " << M << " is not square"; |
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| 170 | it_warning(err.str()); |
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| 171 | } else { |
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| 172 | for ( int i = dim-1; i >= 0; i-- ) { |
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| 173 | // subdeterminanty |
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| 174 | if ( det(M(0,i,0,i)) <= 0 ) { |
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| 175 | return false; |
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| 176 | } |
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| 177 | } |
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| 178 | return true; |
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| 179 | } |
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| 180 | return false; |
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| 181 | } |
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| 182 | |
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| 183 | |
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| 184 | |
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| 185 | |
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| 186 | }; |
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| 187 | |
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| 188 | #endif /* QUADRATICMINIMALIZATOR_H */ |
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