Approximate Optimal Control For A Class Of Nonlinear Interconnected Systems Based On Adaptive Dynamic Programming

With the development of control science,the control methods of linear systems are difficult to meet the control design requirements of complex systems,so the nonlinear direction of system control has increasingly become the focus of attention.In the nonlinear system,nonlinear interconnected system is a very representative kind of system,which widely exists in power,communication and other fields.The problems of high coupling interconnection term,nonlinear link and limited control input in the system seriously affect the controller design and stability guarantee of the system,and greatly increase the complexity and difficulty of controller design.Based on Lyapunov stability theory and adaptive dynamic programming method,an effective stabilization control strategy is proposed for a class of nonlinear interconnected systems.Firstly,the research background of approximate optimal control for nonlinear interconnected systems is introduced,and some theories and methods involved in the controller design process,such as adaptive dynamic programming,neuron and neural network,are briefly introduced.Secondly,for a class of nonlinear interconnected systems with matching interconnections,a new decentralized event triggered controller based on adaptive dynamic programming is proposed to ensure the approximate optimal stabilization and stability of the system.By designing a new decentralized control structure,the decoupling problem of interconnected system controller design is avoided.By using the event triggered control method,the frequent action of the controller is avoided and the control frequency is reduced.By means of adaptive dynamic programming,the problem that the Hamiltonian Jacobian Behrman equation is difficult to solve in nonlinear optimal control is avoided.By Lyapunov theory,it is proved that all signals of the closed-loop system are uniformly ultimately bounded under the designed controller.The effectiveness of the proposed control method is verified by computer simulation.Finally,for a class of mismatched interconnected nonlinear systems with control constraints,a new decentralized input constrained controller is proposed based on adaptive dynamic programming,which guarantees the approximate optimal stabilization and stability of the system.Aiming at the mismatched interconnections in the system,a decentralized auxiliary control structure is designed to deal with the mismatched interconnections.Aiming at the problem of limited controller,a nonlinear transfer function is designed to avoid the influence of controller system on stability.The Hamilton Jacobi Behrman equation of optimal control is solved by adaptive dynamic programming.Through Lyapunov method,it is proved that the closed-loop system is uniformly ultimately bounded under the proposed control strategy,and the effectiveness of the designed controller is verified by a software simulation example.