On Command Filter Adaptive Optimal Control For Nonlinear Systems

With the development of modern control theory,people put forward higher requirements for the performance of control systems.The unmodeled dynamics is an important factor affecting the stability of the system,but only considering the steady-state performance of the system cannot meet the needs of the practical problems,and the preset performance can consider both the steady-state performance and the transient performance of the system.In recent years,adaptive optimal control and event-triggered control based on dynamic surface control reference are one of the hot issues in control theory research,and their research has important academic value.However,the traditional dynamic surface control method has the shortcomings of the first-order filtering error and the difficulty of determining the variables contained in the black-box function.In this paper,several adaptive optimal control schemes are proposed by introducing error compensation signals for nonlinear systems with unmodeled dynamics and preset performance,combined with command filter technology,event-triggered control technology and dynamic surface control method.The main research contents are as follows:Firstly,an adaptive optimal control strategy based on command filter technology is proposed for a class of strict-feedback nonlinear systems.The whole controller design consists of feedforward controller and feedback controller.In the feedforward controller,the improved DSC method and the second-order command filter technology are used to successfully replace the first-order filter in the classical DSC method,the assumption that the second-order filter input is bound is eliminated.In the feedback controller,the ADP algorithm is used to handle the optimal control problem,and the neural network is employed to approximate the unknown cost function and the optimal control signals at each step of the recursion.A simulation example are employed to verify the availability of the scheme.Secondly,the problem of command filter and event-triggered mechanism based adaptive neural optimal control is discussed for a class of nonlinear systems in the presence of unmodeled dynamics in strict-feedback form.The overall controller design is composed of feedforward controller and feedback controller as well as event-triggered controller design.In the first part,the feedforward controller is constructed by exploiting command filter and introducing the compensation error,and the first-order filter in the classical DSC technology is replaced by utilizing the second-order filter.In the second part,adaptive ADP algorithm is used to estimate the unknown optimal index function and optimal control signal by the aid of the capability of neural networks.In the third part,based on the feedforward and feedback controllers,an adaptive event-triggered control is developed to avoid the occurrence of Zeno behavior.Two simulation examples are exploited to verify the availability of the scheme.Thirdly,an optimal DSC strategy based on command filter is proposed for uncertain pure-feedback nonlinear systems with prescribed performance.The adaptive prescribed performance tracker is constructed by hyperbolic tangent function,which ensures that tracking error converges to a predetermined range.The global controller is composed of feedforward controller and feedback controller.In the first part,the second-order command filter and the introduction of error compensation mechanism replace the first-order filter in the classical DSC method,which simplifies the design process of the controller and reduces the use of black box functions by using the properties of Gaussian functions.In the second part,the ADP algorithm is employed to solve the optimal control problem of the controlled system,and the three-layer neural network is used to approximate the unknown optimal indicator function and the optimal control signal.Two numerical examples are exploited to demonstrate the feasibility of the scheme.