// Copyright (C) 2015 Davis E. King (davis@dlib.net) // License: Boost Software License See LICENSE.txt for the full license. #undef DLIB_MPC_ABSTRACT_Hh_ #ifdef DLIB_MPC_ABSTRACT_Hh_ #include "../matrix.h" namespace dlib{template <longS_,longI_,unsignedlonghorizon_ > classmpc{/*! REQUIREMENTS ON horizon_ horizon_ > 0 REQUIREMENTS ON S_ S_ >= 0 REQUIREMENTS ON I_ I_ >= 0 WHAT THIS OBJECT REPRESENTS This object implements a linear model predictive controller. To explain what that means, suppose you have some process you want to control and the process dynamics are described by the linear equation: x_{i+1} = A*x_i + B*u_i + C That is, the next state the system goes into is a linear function of its current state (x_i) and the current control (u_i) plus some constant bias or disturbance. A model predictive controller can find the control (u) you should apply to drive the state (x) to some reference value, or alternatively to make the state track some reference time-varying sequence. It does this by simulating the process for horizon_ time steps and selecting the control that leads to the best performance over the next horizon_ steps. To be precise, each time you ask this object for a control, it solves the following quadratic program: min sum_i trans(x_i-target_i)*Q*(x_i-target_i) + trans(u_i)*R*u_i x_i,u_i such that: x_0 == current_state x_{i+1} == A*x_i + B*u_i + C lower <= u_i <= upper 0 <= i < horizon_ and reports u_0 as the control you should take given that you are currently in current_state. Q and R are user supplied matrices that define how we penalize variations away from the target state as well as how much we want to avoid generating large control signals. Finally, the algorithm we use to solve this quadratic program is based largely on the method described in: A Fast Gradient method for embedded linear predictive control (2011) by Markus Kogel and Rolf Findeisen !*/ public: const staticlongS = S_; const staticlongI = I_; const staticunsignedlonghorizon = horizon_;mpc( ); /*! ensures - #get_max_iterations() == 0 - The A,B,C,Q,R,lower, and upper parameter matrices are filled with zeros. Therefore, to use this object you must initialize it via the constructor that supplies these parameters. - #get_target_error_threshold() == -1 !*/mpc( const matrix<double,S,S>& A, const matrix<double,S,I>& B, const matrix<double,S,1>& C, const matrix<double,S,1>& Q, const matrix<double,I,1>& R, const matrix<double,I,1>& lower, const matrix<double,I,1>& upper ); /*! requires - A.nr() > 0 - B.nc() > 0 - A.nr() == A.nc() == B.nr() == C.nr() == Q.nr() - B.nc() == R.nr() == lower.nr() == upper.nr() - min(Q) >= 0 - min(R) > 0 - min(upper-lower) >= 0 ensures - #get_A() == A - #get_B() == B - #get_C() == C - #get_Q() == Q - #get_R() == R - #get_lower_constraints() == lower - #get_upper_constraints() == upper - for all valid i: - get_target(i) == a vector of all zeros - get_target(i).size() == A.nr() - #get_max_iterations() == 10000 - #get_epsilon() == 0.01 - #get_target_error_threshold() == -1 !*/ const matrix<double,S,S>&get_A( ) const; /*! ensures - returns the A matrix from the quadratic program defined above. !*/ const matrix<double,S,I>&get_B( ) const; /*! ensures - returns the B matrix from the quadratic program defined above. !*/ const matrix<double,S,1>&get_C( ) const; /*! ensures - returns the C matrix from the quadratic program defined above. !*/ const matrix<double,S,1>&get_Q( ) const; /*! ensures - returns the diagonal of the Q matrix from the quadratic program defined above. !*/ const matrix<double,I,1>&get_R( ) const; /*! ensures - returns the diagonal of the R matrix from the quadratic program defined above. !*/ const matrix<double,I,1>&get_lower_constraints( ) const; /*! ensures - returns the lower matrix from the quadratic program defined above. All controls generated by this object will have values no less than this lower bound. That is, any control u will satisfy min(u-lower) >= 0. !*/ const matrix<double,I,1>&get_upper_constraints( ) const; /*! ensures - returns the upper matrix from the quadratic program defined above. All controls generated by this object will have values no larger than this upper bound. That is, any control u will satisfy min(upper-u) >= 0. !*/ const matrix<double,S,1>&get_target( constunsignedlongtime ) const; /*! requires - time < horizon ensures - This object will try to find the control sequence that results in the process obtaining get_target(time) state at the indicated time. Note that the next time instant after "right now" is time 0. !*/voidset_target( const matrix<double,S,1>& val, constunsignedlongtime ); /*! requires - time < horizon ensures - #get_target(time) == val !*/voidset_target( const matrix<double,S,1>& val ); /*! ensures - for all valid t: - #get_target(t) == val !*/voidset_last_target( const matrix<double,S,1>& val ); /*! ensures - performs: set_target(val, horizon-1) !*/doubleget_target_error_threshold( ) const; /*! ensures - The target error terms in the objective function with values less than get_target_error_threshold() are ignored. That is, the trans(x_i-target_i)*Q*(x_i-target_i) terms with values less than this are dropped from the objective function. Therefore, setting get_target_error_threshold() to a value >= 0 allows you to encode a control law that says "find me the controls that make the target error less than or equal to this at some point, but I don't care what happens at times after that." !*/voidset_target_error_threshold( constdoublethresh ); /*! ensures - #target_error_threshold() == thresh !*/unsignedlongget_max_iterations( ) const; /*! ensures - When operator() is called it solves an optimization problem to get_epsilon() precision to determine the next control action. In particular, we run the optimizer until the magnitude of each element of the gradient vector is less than get_epsilon() or until get_max_iterations() solver iterations have been executed. !*/voidset_max_iterations(unsignedlongmax_iter ); /*! ensures - #get_max_iterations() == max_iter !*/voidset_epsilon(doubleeps ); /*! requires - eps > 0 ensures - #get_epsilon() == eps !*/doubleget_epsilon( ) const; /*! ensures - When operator() is called it solves an optimization problem to get_epsilon() precision to determine the next control action. In particular, we run the optimizer until the magnitude of each element of the gradient vector is less than get_epsilon() or until get_max_iterations() solver iterations have been executed. This means that smaller epsilon values will give more accurate outputs but may take longer to compute. !*/ matrix<double,I,1>operator() ( const matrix<double,S,1>& current_state ); /*! requires - min(R) > 0 - A.nr() == current_state.size() ensures - Solves the model predictive control problem defined by the arguments to this object's constructor, assuming that the starting state is given by current_state. Then we return the control that should be taken in the current state that best optimizes the quadratic objective function defined above. - We also shift over the target states so that you only need to update the last one (if you are using non-zero target states) via a call to set_last_target()). In particular, for all valid t, it will be the case that: - #get_target(t) == get_target(t+1) - #get_target(horizon-1) == get_target(horizon-1) !*/};}#endif // DLIB_MPC_ABSTRACT_Hh_