Adaptive Control of Unknown Pure Feedback Systems with Pure State Constraints

TL;DR

This paper introduces an adaptive backstepping control method for unknown pure feedback systems with state constraints, utilizing neural networks, Barrier Lyapunov Functions, and disturbance observers to ensure robust tracking.

Contribution

It is the first to combine adaptive backstepping with neural network approximation and Barrier Lyapunov Functions for pure feedback systems with state constraints.

Findings

Successfully maintains state constraints during tracking.

Demonstrates robustness against unknown disturbances.

Validates approach through simulation on a third-order system.

Abstract

This paper deals with the tracking control problem for a class of unknown pure feedback system with pure state constraints on the state variables and unknown time-varying bounded disturbances. An adaptive controller is presented for such systems for the very first time. The controller is designed using the backstepping method. While designing it, Barrier Lyapunov Functions is used so that the state variables do not contravene its constraints. In order to cope with the unknown dynamics of the system, an online approximator is designed using a neural network with a novel adaptive law for its weight update. In the stability analysis of the system, the time derivative of Lyapunov function involves known virtual control coefficient with unknown direction and to deal with such problem Nussbaum gain is used to design the control law. Furthermore, to make the controller robust and computationally inexpensive, a novel disturbance observer is designed to estimate the disturbance along with neural network approximation error and the time derivative of virtual control input. The effectiveness of the proposed approach is demonstrated through a simulation study on the third-order nonlinear system.