Static Output Feedback Control For Linear Systems Based On Reinforcement Learning

The general idea of optimal control is to find an optimal control scheme so that the system can optimally achieve the desired goal.All state information needs to be known in the state feedback,but in fact,state information is often difficult to obtain,and what can be directly obtained is the measurable input and output data information.However,the use of state observers will bring about increased cost and errors,so it is necessary to study the static output feedback control method.Solving linear quadratic optimal problems usually requires knowledge of system dynamics,but they are often difficult to obtain in reality.Reinforcement learning is a method that adjusts its own strategy by perceiving the environment.In recent years,it has been used in control theory to design data-based algorithms.Therefore,this paper will study the static output feedback problem of linear systems based on reinforcement learning.The main research of this paper is and contributions are as follows:Firstly,for the problem of unmeasurable state in state feedback,the analysis linear system uses static output feedback control to achieve optimal conditions.For continuous systems,analysis of the rationality of using a static output feedback control law to achieve optimal conditions,based on solving a Riccati equation and a Lyapunov equation,and optimal conditions are given for discrete systems.Bellman’s principle of optimality proves its rationality.Secondly,an easy-to-implement iterative algorithm is obtained by decoupling the existing coupled nonlinear Lyapunov equations.and its rationality and convergence are proved;for discrete systems,a modelbased policy iterative algorithm is designed,and its convergence been verified.Then,the proposed iterative algorithm is simulated.In order to make the proposed algorithm more convincing,the simulation verification is carried out for the case where the output matrix is a square matrix and a non-square matrix,to illustrate the effectiveness of the algorithm.Finally,for the problem of unknown system dynamics,a data-based integral reinforcement learning algorithm is proposed for continuous systems,and its specific implementation process is given by using Kronecker product.For discrete systems,the solution of the Riccati equation is converted into the optimal Q function,and the rationality of the algorithm is evaluated.Finally,the validity of the algorithm is verified by simulation verification.In this paper,the static output feedback control problem of linear system is studied,and based on this,and on this basis,the algorithm based on model and data is studied,which has important theoretical significance and practical application value.