PI-based Self-learning Optimal Control Of Linear Singularly Perturbed Systems

Singularly perturbated systems?SPSs?are two-time-scale systems with fast and slow dynamics.They exist widely in power systems,chemical processes,and robotics.The existing optimal control methods of SPSs are mainly limited to the case where the model parameters are known.Adaptive dynamic programming?ADP?is a self-learning technology that can design optimal controller without completely knowing the system dynamics.ADP has been widely used to solve problems related to optimal control of large systems such as weakly coupled systems,interconnected systems.Due to the coexistence of slow and fast phenomena,the application of existing self-learning optimal control methods directly to SPSs with unknown models will lead to“ill-conditioned numerical problem”.For unknown linear SPSs,ADP method and two-time-scale structure of the systems are combined to study the self-learning optimal control method based on policy iteration?PI?.In this thesis,the goal is to overcome the“ill-conditioned numerical problem”of the conventional self-learning control method and propose a well-posed online learning algorithm.The main work is summarized as follows:1.An online learning algorithm based on PI is designed to solve the optimal state regulation problem of unknown linear SPSs.Firstly,the Lyapunov equation involved in the traditional Kleinman algorithm is reconstructed by means of the structural characteristics of the cost function parameter matrix,and a revised Kleinman algorithm is proposed.Secondly,according to the integral Bellman equation and the two-time-scale characteristic of the systems,an online PI algorithm is designed.Thirdly,the convergence of the algorithm and the stability of the closed-loop system are proved by the analysis of the equivalence of two algorithms.Finally,the simulation results show that the proposed method has better robustness.2.An online learning algorithm based on PI is designed to solve the mixed H₂/H_?control problem of unknown linear SPSs.Firstly,the Lyapunov equations involved in the recursive iterative algorithm are reconstructed by means of the structural characteristics of the cost function parameter matrices,and an offline algorithm with any stable feedback gain as the initial condition is proposed.Secondly,a well-posed online PI algorithm is designed by using the real-time measured data and singular perturbation parameter.Thirdly,the convergence of the online algorithm and the stability of the closed-loop system are analyzed.Finally,the feasibility of the proposed method is verified by numerical simulation.3.An online learning algorithm based on PI is designed to solve the optimal output tracking control problem of unknown linear SPSs.Firstly,an augmented model composed of reference trajectory and original system is constructed to transform the tracking problem into the regulator problem of augmentation system.Secondly,a data-based well-posed PI algorithm is designed to learn the feedforward and feedback control gains.Thirdly,the convergence of the proposed online algorithm and the stability of the closed-loop system are proved.Finally,a simulation example of DC motor system is used to verify the effectiveness of the proposed method.