root/applications/dual/src/arx1_ctrl.h @ 707

#ifndef ARX_CTRL_H
#define ARX_CTRL_H

#include <design/ctrlbase.h>
using namespace bdm;

/*! exact controller for system \f$ y_{t+1} = y_{t} + b u_{t} + \sigma e_t \f$

From \f$ E\{y_{ref}\} = E\{ y_{t} + b u_{t} \} \f$, the optimal control action is:
\f[ u_t = (y_{ref} - y_{t})/b \f]

*/ 

class exact_ctrl: public Controller {
        protected:
                //! target value of y
                double yr;
                //! parameter b (or its estimate)
                double b;
        public:
                void set_b (const double b0){b=b0;}
                //! data in ctrlaction are only past outputs yt
                vec ctrlaction(const vec &yt){
                        vec ut(1);
                        if (abs(b)<1e-2) {
                                ut= 0.1*randn();
                        } else {
                                ut = (yr-yt)/b;
                        }
                        return ut;
                }
                void from_setting(const Setting &set){
                        Controller::from_setting(set);
                        UI::get(yr,set,"yr",UI::compulsory);
                        UI::get(b,set,"b",UI::compulsory);
                        validate();
                }
                void validate() {       }
};
UIREGISTER(exact_ctrl);

/*! adaptive CE controller for \f$ y_{t+1} = y_{t} + b u_{t} + \sigma e_t \f$

From \f$ E\{y_{ref}\} = E\{ y_{t} + b u_{t} \} \f$, the optimal control action is:
\f[ u_t = (y_{ref} - y_{t})/b \f]

Using certainty equivalent approach, i.e. \f$ b= E(b|y_t, u_t, \ldots )\f$, which is 
estimated using ARX model. This class is not truly appropriate since it estimates also \f$ \sigma \f$


*/

class ce_ctrl: public exact_ctrl {
        protected:
                //! estimator
                ARX est;
                //! vector of "dyad" for estimation
                vec Psi;
                //! remember last action - for estimation
                double utm;
                //! remember last input - for estimation
                double ytm;
        public:
                //! expected input is yt
                virtual void adapt(const vec &yt){
                        //prepare data for ARX
                        Psi(0) = yt(0)-ytm;
                        Psi(1) = utm;
                        // do estimation
                        est.bayes(Psi);
                        // save estimate b = E(b);
                        b = est.posterior().mean()(0); // first
                }
                //! same as exact control, but stores ut as utm
                vec ctrlaction(const vec &yt){
                        vec ut=exact_ctrl::ctrlaction(yt);
                        // remember last ut for estimation
                        utm=ut(0);
                        ytm=yt(0);
                        return ut;
                }
                void from_setting(const Setting &set){
                        Controller::from_setting(set);
                        UI::get(yr,set,"yr",UI::compulsory);
                        double b0;
                        UI::get(b0,set,"b0",UI::compulsory);
                        double P0;
                        UI::get(P0,set,"P0",UI::compulsory);
                        
                        mat V0(2,2);
                        V0(0,0) = 0.1;
                        V0(1,0) = b0;
                        V0(0,1) = b0;
                        V0(1,1) = P0;
                        
                        est.set_statistics(1,V0);
                        est.set_constant(false);
                        validate();
                }
                void validate(){
                        Psi = zeros(2);
                        LIDs = zeros_i(1);
                }
                virtual void log_add ( logger &L, const string &name = "" ) {
                        LIDs ( 0 ) = L.add ( RV("bhat",1) );
                }
                virtual void logit ( logger &L ) {
                        L.logit ( LIDs ( 0 ), b );
                }
                
};
UIREGISTER(ce_ctrl);

#endif //ARX_CTRL