The Research On Online Parameter Identification-based Optimal Control Of Nonlinear Systems

Most actual systems exhibit highly nonlinear and strong coupling characteristics,which may lead to degradation or instability of system performance.In view of the urgent demand for efficient utilization of social resources and promote sustainable development,the design of nonlinear system control methods aim to maximize system performance or minimize energy consumption while ensuring system stability.However,traditional optimal control methods typically rely on the Persistency of Excitation(PE)conditions,whether applied to single-agent or multi-agent systems.This requirement usually presents challenges in practical engineering applications.Relaxing the dependency on the PE condition remains a formidable issue within the filed of optimal control.Furthermore,the large-scale and nonlinear coupling characteristics inherent in actual systems pose considerable difficulties in accurately modeling these systems,thereby complicating the application of model-dependent optimal control approaches.To address these challenges,this Dissertation introduces a novel optimal control algorithm for the nonlinear systems optimal control problem with unknown dynamics under weak PE conditions by employing parameter identification technology and adaptive dynamics programming method.Additionally,this Dissertation enhances the exisit learning method based on parameter identification,resulting in improved control performance in terms of convergence speed and transient behavior.The main research results of this Dissertation are summarized as follows:1.An optimal control problem is studied for affine nonlinear systems based on Kreisselmeier’s regression extension and mixing technique.A novel identifier-critic framework is presented for achieving optimal control of nonlinear systems with completely unknown dynamics.The identifier networks are established to estimate the unknown dynamics,while the critic networks are utilized to formulate the performance index function.Unlike the classical identifier-critic structure,the neural networks’ weight estimation problem is transformed into a parameter estimation problem in this Dissertation,and a new weights update law is designed by using Kreisselmeier’s regression extension and mixing technique,ensuring convergence of the weight estimation error under an interval excitation(IE)condition in a faster speed and stronger transient performance way.Additionally,an precise lower bound for the new regressor is theoretically obtained.The convergence to the optimal controller and the stability of the closed-loop system are theoretically demonstrated via Lyapunov theory.2.An optimal control problem is studied for affine nonlinear systems based on dynamic regression extension and mixing technique.A new identifier–critic optimal control framework is designed using the dynamic regression extension and mixing technique.In the process of network learning,the selection range of filter operators in the implementation of Kreisselmeier’s regression extension and mixing is expanded.Additionally,careful consideration is given to the error term generated by the filter,enabling a more comprehensive theoretical analysis.Furthermore,a new weak PE convergence condition is introduced,and its weak PE property is theoretically demonstrated.Simulation comparisons are conducted between the proposed learning algorithm,the traditional adaptive dynamic programming method relying on PE conditions,and the weak PE adaptive dynamic programming method.The results of these comparisons underscore the superiority of the proposed learning algorithm.3.An optimal control problem is studied for affine nonlinear systems based on improved dynamic regression extension and mixing technique.The focus of this study is to address the issue of transient excitation maintenance in optimal control algorithms by using dynamic regression extended and mixing.To tackle this problem,an improved identifier-critic framework is proposed.This framework integrates neural network linearization and filtering technology,enabling the transformation of the system model reconstruction and optimal control design into a parameter estimation problem framed as a linear regression equation.Additionally,an auxiliary system is introduced within the dynamic regression extension and mixing technology to generate a new scalar regression with improved excitation performance.The weight update law is designed based on this new scalar regression to ensure long-time excitation maintenance of the system.The proposed optimal control algorithm is realize under IE conditions.Significantly,unlike other optimal control methods operating under IE conditions,the proposed algorithm has the capability to transform the original regression,which may suffer from insufficient excitation,into a scalar regression that satisfies PE conditions.Finally,the effectiveness of the improved algorithm and its ability to track time-varying parameters are verified through simulation.4.An optimal consensus problem of multi-agent systems is studied based on parameter identification technology.The optimal control method,incorporating parameter identification technology,is applied to tackle the optimal consensus control problem in a class of nonlinear leader-follower multi-agent systems,where the dynamics and states of the leader are potentially unknown.To address this challenge,a distributed control scheme based on Kreisselmeier’s regressor extension and mixing technique is developed,enabling the estimation of dynamic parameters and leader states for each agent.Subsequently,the optimal consensus control problem is transformed into an optimal tracking control problem of the leader.A control method is introduced that combines critic network with a weights update mechanism based on parameter identification techniques,facilitating online optimization of each controller.The convergence of the algorithm and the stability of the closed-loop system are theoretically proven.Finally,the effectiveness of the proposed distributed adaptive control method in resolving the optimal consensus problem of multi-agent systems is confirmed through simulation.