Safety‐constrained robust adaptive control for a class of MIMO non‐linear systems

Abstract

This study proposes two new safety‐constrained robust indirect adaptive control schemes for a class of multi‐input multi‐output non‐linear systems subject to unstructured additive model uncertainties and external disturbances. The controllers are designed using a novel error transformation and a new asymptotically stable closed‐loop non‐linear error dynamics. The model uncertainties of the actual system are approximated by constructing a neural network‐based auxiliary observer dynamics. The weights of the neural network are updated using a robust Lyapunov stable weight update rule. Using the estimation information of model uncertainties, two different asymptotically and finite‐time exponentially stable tracking controllers are designed to minimise the error between auxiliary observer states and reference signals. It is proven that the closed‐loop states of the actual system will remain bounded by the imposed state constraints and the steady‐state tracking error of the system will converge asymptotically (or exponentially in finite time) to a user‐defined domain. The beauty of the proposed control designs lies in the fact that they are easy to design and implement, and provide design freedom to impose constraints on an individual component of the system states. The effectiveness of the proposed techniques is shown by controlling a two‐link robot manipulator in a constrained environment.