Backstepping Adaptive Robust Output Feedback Control For Uncertain Nonlinear Systems

Uncertain nonlinear systems are widely used in industrial manufacturing,national defense construction and other practical production,such as ships,aircraft,mechanical arms,hydraulic systems,etc.To meet engineering needs,the controlled system always expects to have faster convergence speed,higher tracking accuracy,or other superior performance indicators on the basis of achieving stability.However,due to various factors such as environmental interference,modeling errors,actuator failures,and physical characteristics,the controlled system inevitably faces problems such as parameter uncertainty,disturbances,or constraints,which greatly affect system performance.Therefore,it is of great theoretical significance and application prospect to study the control problems such as disturbance suppression of uncertain nonlinear systems.This topic takes the influence of parameter uncertainties,external disturbances and constraints on the strict feedback nonlinear system as the starting point,and combines the cascade extended state observer,dynamic surface control technology,obstacle Lyapunov function,disturbance observer,finite time command filter and other methods to study the adaptive robust output feedback control strategy to ensure the stability and robustness of the system,Implement control strategies to track system performance.The research mainly includes the following three aspects:(1)The influence mechanism of external disturbance and parameter uncertainty on strict feedback nonlinear systems is studied.Without speed information measurement,a group of cascaded extended state observer are constructed to estimate the disturbance,and an adaptive robust output feedback control strategy to suppress unknown external disturbance is proposed.By introducing parameter adaptive design into the cascaded extended state observer,the system parameter uncertainty is compensated,the impact of uncertainties on system performance is reduced,the steady-state tracking control error is reduced,and the continuous estimation signal is generated to avoid input chattering.Furthermore,in order to avoid the "differential explosion" caused by the repeated derivation of virtual control laws in backstepping technology,the recursive sliding mode dynamic surface method is used to simplify the complexity of control algorithm design and improve system robustness.Secondly,using a nonlinear gain function instead of a linear gain function in the control algorithm improves system performance and effectively compensates for input saturation limitations caused by high gain.Finally,the effectiveness of the proposed control method was analyzed and verified through Lyapunov stability theory and simulation experiments,proving that the above control method can ensure the stability of the closed-loop system and has good tracking performance and anti-interference ability.(2)The backstepping adaptive robust output feedback control strategy for nonlinear systems with output constraints and state constraints uncertainties is studied to solve the negative impact of complex uncertainties on the system performance and realize the tracking control performance of nonlinear systems under constraints.The backstepping control framework designed by combining obstacle Lyapunov function and dynamic surface control technology eliminates the problem of repeated derivation of virtual control laws and solves constraint constraints.In order to alleviate the conservatism of traditional filter gain selection,an adaptive gain nonlinear filter is introduced into the control algorithm.In addition,disturbance observers are used to estimate disturbances,and the design of parameter adaptive laws reduces the impact of uncertain factors on system performance.Through Lyapunov stability theory and simulation experiments,the proposed control strategy can ensure that the boundedness of output constraints and state constraints makes the tracking error of the closed-loop system converge to a small neighborhood of zero,and all signals are ultimately known to be bounded and stable,ensuring significant tracking control performance.(3)The finite time backstepping adaptive robust output feedback control strategy for uncertain nonlinear systems is studied to realize finite time tracking control.Considering the transient performance of the control system,the prescribed performance control theory is used to converge the tracking error signal to the prescribed small compact set,so that the convergence speed and steady-state error meet the predetermined performance limits.Secondly,in order to ensure the fast approximation of the derivative of the virtual signal and weaken the chattering phenomenon,a backstepping adaptive control algorithm is designed based on the finite time command Filter design.Introduce an error compensation mechanism to quickly eliminate the impact of filtering errors generated by the filter.Applying disturbance observers to the design of tracking error compensation to reduce the impact of disturbances on system performance.Derive an update law for adaptive parameters based on Lyapunov stability conditions to achieve uniformly bounded stability of the system.Through simulation experiments,the proposed finite time control strategy has outstanding advantages such as high tracking accuracy,fast convergence speed,and strong anti-interference ability.