A comprehensive control paradigm for prescribed performance attainment in complex nonlinear systems

Abstract

This paper presents a comprehensive control framework tailored for achieving Prescribed Performance Control (PPC) in the context of complex nonlinear systems, addressing multifaceted challenges prevalent in control design. The focus is on a control scenario characterized by the simultaneous presence of nonlinearity, external disturbances, time delay, and unknown control direction—issues that pose considerable obstacles for existing solutions. To surmount these challenges, our proposed approach integrates well-established techniques, including neural networks, Nussbaum-type gains, and adaptive control strategies within a unified control design framework. The specific technical challenge addressed in this work involves the effective management of these intricate complexities in Single-Input Single-Output (SISO) systems. Our contributions extend the theoretical foundations, presenting an ideal PPC control design and introducing two adaptive neural network-based control methods capable of accommodating both known and unknown control directions. Utilizing Lyapunov-Krasovskii functionals, we showcase a unique integration that surpasses a mere combination of individual techniques. This work advances the theoretical underpinnings of control engineering tailored for real-world scenarios. The proposed controller’s efficacy is validated through rigorous simulations and compared with recent results and benchmark PPC controllers, establishing its superiority in addressing the intricacies of complex control scenarios.