Model reference-based control with guaranteed predefined performance for uncertain strict-feedback systems

Abstract

A wide range of practical applications in robotics and automation can be modeled in a class of uncertain and nonlinear strict-feedback (SF) systems. In SF systems, the hierarchical influence of control inputs on state dynamics renders each level dependent on preceding control actions. However, designing a robust, performance-guaranteed controller is challenging in real-world applications due to the complexities introduced by time- and state-varying uncertainties and the difficulty in computing analytic derivatives in SF systems. To address this challenge, this study introduces a novel model reference-based control (MRBC) framework that applies locally to each subsystem (SS) of SF systems, to ensure output tracking performance within the specified transient and steady-state response criteria. This framework includes (1) novel homogeneous adaptive estimators (HAEs) designed to match the uncertain nonlinear SF system to an ideal reference model, enabling easier analysis and control design at the SS level, and (2) model-based homogeneous adaptive controllers enhanced by logarithmic barrier Lyapunov functions (HAC-BLFs), intended to control the reference model provided by HAEs in each SS, while ensuring the prescribed tracking responses under control amplitude saturation. The inherently robust MRBC achieves uniformly exponential stability using a generic stability connector term, which addresses dynamic interactions between the adjacent SSs. The parameter sensitivities of HAEs and HAC-BLFs in the MRBC framework are analyzed, focusing on the system’s robustness and responsiveness. The proposed MRBC framework is experimentally validated on an electromechanical linear actuator system with an uncertain SF form, by comparison with two high-performance adaptive control strategies under loading disturbance forces challenging 0–95% of its capacity.