On Command Filter Based Adaptive Control For Con-Strained Nonlinear Systems With Time Delay

The issue of input delay is widely presented in industrial automation,power machine clusters,and multi-agent systems.The input delay can arise from factors such as the response time of actuators,delays in signal processing and communication,as well as computation and execution time of the controller.Input delay can impact the control performance of the system and even lead to system instability.In recent years,the research of adaptive control for nonlinear systems with input delay has been a hot topic in the control field.However,there are still many problems to be solved when applying command filtering adaptive control method to systems with input delay,and when considering characteristics such as quantization,event triggering,and input saturation in systems with input delay.Therefore,this paper focuses on uncertain nonlinear systems with input delay,considering the system’s characters of state constraints,unmodeled dynamics,and input saturation.By integrating techniques such as quantized control,event-triggered control,neural network control,finite-time control,and adaptive control,several dynamic surface control(DSC)schemes based on command filter are proposed.The main work of this paper is as follows:First,an adaptive control scheme based on command filtering is proposed for a class of stochastic nonlinear systems with input delays and full state constraints of stochastic nonlinear systems.Combining with the command Filter design,a reasonable signal compensator is designed to solve the problem that the variables contained in the black box function in the dynamic surface are difficult to describe accurately.Stochastic input state stability and supply changing functions are used to handle stochastic unmodeled dynamics.We have improved the definition of state constraints in the stochastic sense and utilized Pade approximation and nonlinear mapping methods to transform constrained time-delay systems into unconstrained time-delay systems.For the designed command filter,it is unnecessary to assume that the error between the output and the input is bounded,thus avoiding unreasonable assumptions about the boundedness of the designed virtual control.Simulation experiments have verified the effectiveness of the control scheme.Secondly,a finite-time control scheme based on command filtering is proposed for a class of nonlinear systems with unknown input delays and discontinuous inputs.Input discontinuity makes traditional time delay processing methods based on derivative impossible to apply,and the unknown time delay also increases the design difficulty.This paper proposes a new compensator design method based on the use of signal compensators to handle the black box function in dynamic surface control(DSC),which can simultaneously handle command filtering compensation and unknown discontinuous time delay compensation.We design a suitable Lyapunov functional and prove that all signals are semi-globally practicaly finite-time bounded.Thirdly,the finite-time control problem of multi-agent system with input saturation and unknown input delay is studied.Based on the systematic analysis of the possible different and unknown input delays among the followers of the current multi-agent system,a new command filtering error signal is designed.By using this error signal,not only does it solve the problem of different input delays among followers,but it also solves the problem of input non differentiability caused by input saturation.By using graph theory and DSC based on command filtering,the collaborative control between various subsystems and leaders is achieved.Numerical simulations demonstrate the effectiveness of this scheme.