Finite-time Adaptive Dynamic Surface Control For Nonlinear Systems With Unmodeled Dynamics

With the rapid development of modern industry,people continue to study nonlinear control in depth.In the process of research,it is often necessary to model the system.However,modeling errors often appear in the mathematical modeling of the system,which will have a negative impact on the performance and control accuracy of the system,and even cause instability of the system.Therefore,in the process of controller design,it is very important to consider unmodeled dynamics.Finite-time control has the advantages of fast convergence speed,strong anti-interference and high control precision,which has been widely concerned by scholars in recent decades.The key characteristic of finite time control is that the state of the system reaches equilibrium in finite time,and then remains in equilibrium.Therefore,the study of finite time adaptive dynamic surface control(DSC)for nonlinear systems with unmodeled dynamics is of great significance.In this paper,a nonlinear filter is constructed for several classes of nonlinear systems with input quantization,state unmodeled dynamics,full state constraints,time delay and preset performance.Radial basis functions(RBFNNs)are used to approximate unknown smooth functions.Combined with Young's inequality,several new finite time adaptive DSC strategies are proposed:Firstly,by constructing nonlinear filters and using Young's inequality,a new adaptive finite-time control method is proposed for a class of strict feedback nonlinear systems with full state constraints,unmodeled dynamics and external disturbances.The constrained system is transformed into an unconstrained system by introducing the nonlinear mapping.The radial basis function neural networks are utilized to approximate unknown nonlinear smooth functions.A dynamic signal produced by an auxiliary system is used to deal with unmodeled dynamics.Using modified dynamic surface control technology and finite-time control method,a simple controller is developed.The the singularity problem in the existing finite-time control is removed,and the converging speed of the system is accelerated.Theoretical analysis shows that all signals in the closed-loop system are bounded in finite time.Full state constraints are not triggered.Simulation results of numerical examples show that the proposed approach is effectiveSecondly,by constructing nonlinear filter and using Young's inequality,a new prescribed performance based finite-time adaptive tracking control scheme is developed for a class of pure-feedback nonlinear systems with input quantization and dynamical uncertains.A new quantizer combining the advantages of hysteresis quantizer and uniform quantizer is used to process the input signal.The radial basis function neural networks(RBFNNS)are utilized to approximate unknown nonlinear smooth functions.A dynamic signal produced by an auxiliary system is employed to estimate unmodeled dynamics.By introducing hyperbolic tangent function and performance function,the tracking error falls within the prescribed time-varying constraints.Using modified dynamic surface control(DSC)technology and finite-time control method,a novel finite-time controller is designed,and the singularity problem of differentiating each virtual control in the existing finite-time control is removed.Theoretical analysis shows that all signals in the closed-loop system are semi-globally practical finite-time stable(SGPFTS),and the tracking error converges to a prescribed time-varying region.Simulation results of two numerical examples are provided to illustrate the validity of the proposed control method.Thirdly,by constructing a first-order nonlinear filter and using Young's inequality and using the approximation ability of RBFNNs,a new adaptive finite-time DSC method is proposed for a class of output feedback nonlinear systems with unmodeled dynamics,quantized input delays and dynamic uncertainties.A dynamic signal is used to deal with unmodeled dynamics.Constructing an auxiliary function is used to deal with the impact of input quantization time delay on the entire system.Using modified dynamic surface control and finite-time method,a simple controller is developed,which eliminates the singularity problem in finite time control.Theoretical analysis shows that all signals in the closed-loop system are bounded in finite time.The simulation results show that the proposed scheme is effective.