Robust Adaptive Backstepping Control For A Class Of Nonaffine Nonlinear Systems

Nonaffine nonlinear systems are very common in practice,whose control input functions in a nonlinear and implicit form,posing great challenges to the controller design.This work studies robust adaptive backstepping control scheme for a class of uncertain strict-feedback nonaffine nonlinear systems under several different conditions such as input/output constraints,actuator faults and unmeasurable system states.The research is as follow.First,a nonlinear disturbance observer-based sliding mode dynamic surface control method is proposed for a class of uncertain strict-feedback nonaffine nonlinear systems.To facilitate the design of controllers,taylor series expansion technique is used to make the control input explicit.Based on this,nonlinear disturbance observer is designed to estimate the uncertainties and unknown disturbances in uncertain nonlinear system.Combining dynamic surface control and sliding mode control,sliding mode dynamic surface controllers are proposed,in which the sliding mode variable enhances system robustness and dynamic surface control avoids “explosion of complexity” in traditional backstepping control.The stability is proved by Lyapunov function theory.Simulation results demonstrate that closed-loop system has a good tracking performance.Second,Hermite-polynomial-based recurrent neural network disturbance observer-based backstepping control scheme is proposed for a class of uncertain strict-feedback nonaffine nonlinear systems with input saturation and time-varying output constraints.Approximation method is applied to convert the control input in nonaffine nonlinear system to an explicit expression.Hermite-polynomial-based recurrent neural network disturbance observer is designed to approximate unknown compound disturbance.Asymmetirc barrier Lyapunov function is utilized to design backstepping controllers and the system stability is proved via Lyapunov function theory.Simulation results prove that the proposed control method is effective.Then,an adaptive sliding mode disturbance observer-based fault tolerant control method is proposed for a class of uncertain strict-feedback nonaffine nonlinear systems with actuator faults.The global approximation method is employed to nonaffine nonlinear system to make the control input explicit.Adaptive sliding mode disturbance observer is designed to estimate disturbances.Fault tolerant backstepping ontrollers based on finite-time function theory are proposed and the stability is proved via Lyapunov function.Simulation results demonstrate the good performance of the closed-loop system.Finally,a finite-time disturbance observer-based output feedback integral backstepping control scheme is proposed for a class of uncertain strict-feedback nonaffine nonlinear systems with unmeasurable states.A hyperbolic tangent function-based extended state observer is designed to measure the state of nonaffine nonlinear system,and then system transformation is proceeded to make the control input explicit.For an uncertain nonlinear system with unmeasurable states,finite-time disturbance observer is presented to estimate unknown disturbances and uncertainties.Integral backstepping controllers are designed for this system,and Lyapunov function proves the stability of closed-loop system.Simulation results illustrate stability of the closed-system.