In this paper, a state constraint controller with disturbance compensation is proposed for uncertain nonlinear systems to improve the control performance without violating the full state constraints. A series of extended state observers are designed to estimate disturbances that include the unmodeled dynamics and the modeling errors. To guarantee non-violation of state constraints while compensating the disturbances, based on the backstepping technique, the state constraint controller with extended state observer is proposed by using the barrier Lyapunov function. Then, the stability of the closed-loop system is proved theoretically. Moreover, exponentially asymptotic tracking is achieved when the disturbances are not time-variant. Finally, the effectiveness of the proposed approach is verified by two examples.

Introduction

Disturbances (include the unmodeled dynamics, the modeling errors) always exist in all practical control systems, which may lead to tracking accuracy degradation and even the instability of system. The controller design for nonlinear system has received a great deal of attention due to the requirements in practical applications and theoretical challenges [1]–[۳]. In order to weaken the influence of disturbances, as a main choice, nonlinear robust control has been widely used to attenuate disturbances, such as adaptive robust control [2], sliding mode control [4], super-twisting control [5], continuous nonsingular terminal sliding mode control [6], adaptive control with RISE feedback [7]. Simulations and experiments show that these robust controllers guarantee prescribed output tracking performance. However, large feedback gain might be used to guarantee the high control precision in the abovementioned robust controllers, which may lead to high gain feedback and even system instability. In order to reduce the conservatism of the controller and improve the control performance without high-gain feedback, disturbance compensation in nonlinear systems has been wildly studied [8]–[۱۶]. Various disturbance observers, such as uncertainty and disturbance estimator [10], [15], nonlinear disturbance observer [11], extended state observer [9], [16], and finite-time disturbance observer [13], are designed to estimate the generalized disturbances/uncertainties.