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

• Published in: IET control theory & applications Vol. 14; no. 7; pp. 939 - 951
• Main Authors: Sachan, Kapil, Padhi, Radhakant
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 30.04.2020
• Subjects: adaptive control; asymptotic stability; auxiliary observer states; closed loop systems; closed‐loop nonlinear error dynamics; closed‐loop states; constrained environment; control designs; control system synthesis; external disturbances; finite‐time exponentially stable tracking controllers; Lyapunov methods; manipulators; MIMO nonlinear systems; MIMO systems; multiinput multioutput nonlinear systems; neural network‐based auxiliary observer dynamics; neurocontrollers; nonlinear control systems; novel error transformation; observers; Research Article; robust control; robust Lyapunov stable weight update rule; safety‐constrained robust adaptive control; safety‐constrained robust indirect adaptive control schemes; state constraints; steady‐state tracking error; system states; uncertain systems; unstructured additive model uncertainties; novel error transformation; closed-loop nonlinear error dynamics; manipulators; multiinput multioutput nonlinear systems; MIMO nonlinear systems; asymptotic stability; state constraints; neurocontrollers; system states; robust control; external disturbances; robust Lyapunov stable weight update rule; safety-constrained robust adaptive control; control designs; uncertain systems; adaptive control; control system synthesis; finite-time exponentially stable tracking controllers; neural network-based auxiliary observer dynamics; auxiliary observer states; steady-state tracking error; MIMO systems; closed loop systems; safety-constrained robust indirect adaptive control schemes; nonlinear control systems; constrained environment; closed-loop states; observers; unstructured additive model uncertainties; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2019.0652

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.