Adaptive Optimal Algorithm For Nonlinear Markov Jumping Systems

In this dissertation,the online adaptive optimal control algorithm for continuous-time nonlinear Markov jump systems is studied.Because of the coupling relationship between the subsystems of Markov jump systems,this dissertation introduces the subsystems transformation technology to decouple the coupling relationship between jump systems online On the other hand,consider that neural network has the ability of arbitrary approximation,neural network linear differential inclusion(LDI)technology is introduced in this dissertation to process the nonlinear terms of the nonlinear Markov jump systems to linear terms.And the online LDI representation is realizedAfter subsystems transformation and online LDI representation,based on the adaptive dynamic programming method,this dissertation proposes new online strategy iterative algorithms to solve the H2 and H? optimal controllers of nonlinear Markov jump systems It should be pointed out that the optimal controllers designed in this dissertation only need to know part of the dynamic information,but not all the dynamic information of the systems The specific research contents of this dissertation are as follows1.Non-zero sum differential feedback Nash control problem for a class of linear Markov jump systems is studied.First,the problem is transformed into solving the corresponding coupled algebraic Riccati equation.Then the coupling relationship between subsystems is decoupled by subsystem transformation technique.After that,a new strategy iteration algorithm is designed.Finally,the effectiveness and feasibility of the proposed algorithm are verified by a numerical simulation2.An online adaptive optimal control problem for a class of nonlinear Markov jump systems with partial unknown system dynamics is studied.Applying the neural network LDI techniques,the nonlinear terms are approximately converted to linear forms.By using subsystem transformation schemes,the nonlinear Markov jump systems are transferred to N new coupled linear subsystems.Then a new online policy iteration algorithm is proposed to solve the adaptive optimal controller and the convergence of the algorithm is proved.Finally,a simulation example is given to verify the effectiveness and applicability of the algorithm3.The H optimal control problem for a class of nonlinear Markov jump systems is studied.The nonlinear terms are approximately converted to linear terms by using neural network LDI technique.The Markov jump systems are transferred to N coupled linear subsystems with the same disturbance input by applying subsystems transformation scheme After the above processing,a new online strategy iterative algorithm is proposed to solve the H? adaptive optimal controller,and the convergence of the algorithm is proved.It is worth noting that this algorithm only needs to know partial dynamic information to solve the optimal controller.A simulation example is given to verify the effectiveness and applicability of the algorithmFinally,the conclusion of research contents in this dissertation is given.And the future research directions of related subjects are pointed out.