On Adaptive Quantized Control Of Nonlinear Systems With Time-delay And Constraints

In recent years,time-delay and quantization systems have received great attention in the field of control,and adaptive control for uncertain nonlinear systems has also achieved many good results.However,when nonlinear time-delay systems have unknown control gains and unknown gain signs or simultaneously are required to satisfy state and output constraints or discontinuous control requirements such as quantization control and event-triggered control,many problems still remain to be solved.Therefore,this article comprehensively considers time-delay systems containing constraint conditions or quantitative control,event trigger control demand.And by organically combining the adaptive control,backstepping control,dynamic surface control,quantization control,event trigger control and the method of processing system constraints,and introducing proper Lyapunov-Krasovskii function and integral transformation of input signal etc.,the adaptive control problem is studied for several class of time-delay nonlinear systems with constraint conditions and unmodeled dynamics,and the solution when quantized input and event-triggered signal accompany with time delay characteristics is further presented.The main work of this paper is as follows:Firstly,an adaptive neural networks control is proposed for a class of output-feedback systems with unknown signs and input delay under the condition of output constraint.A coordinate transformation with input integral term and Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain.The uncertainty of the system is approximated by dynamic signal and neural networks(NNs).By designing tuning functions,the adjustment of multi parameters is handled with a single adaptive law.Based on barrier Lyapunov function(BLF)and Lyapunov stability theory,an adaptive tracking control scheme is developed to guarantee the output constraint is not violated,and all the signals are semi-globally uniformly ultimately bounded(SGUUB).Secondly,an adaptive quantized control strategy is proposed for a class of nonlinear systems with state constraints,input unmodeled dynamics and time-varying delay.Design difficulties focus on the fact that the input-quantized actuator possesses both unknown control gain and nonlinear input unmodeled dynamics,and all the states are required to satisfy state constraints.To remove these obstacles,integral barrier Lyapunov functions combined with Nussbaum functions are designed to deal with the unknown control gains and state constraints,and quantized controller combined with normalized signal is developed to tackle the quantized input and input unmodeled dynamics.To avoid the chattering and reduce the quantization error in wide scope of control volume,a novel logarithmic uniform hysteresis quantizer is employed,which has the both advantages of the existing uniform quantizer and hysteresis quantizer.Two examples of practical control systems are conducted to demonstrate the effectiveness of protocol.Thirdly,we investigate control designs for nonlinear systems in strict feedback form with time-varying input delay and unknown control gains.A systematic analysis is presented for the difficulties of controller design caused by unknown input delay and discontinuous input.A novel filtered error signal is designed based on the integration of the past input signals in the maximum time delay interval to deal with the unknown input time delay.With the well-designed Lyapunov-Krasovskii functional,the stability analysis is achieved under the condition that the input time delay finitely grows.The use of dynamic surface control(DSC)effectively simplifies the design of the controller.By constructing an auxiliary tracking error and an auxiliary system,the input quantization and event-triggered control problems with input delay are further solved.The stability analysis shows that all signals are SGUUB.A numerical simulation example in three cases shows the effectiveness of the schemes.