Asymptotic Adaptive Tracking Control Based on Disturbance Observer for Non-Strict Feedback Nonlinear Systems

This paper proposes an innovative composite anti-disturbance asymptotic tracking control strategy for a class of nonlinear non-strict feedback systems facing unknown nonlinearities and external disturbances. Based on the separation principle, a new adaptive learning disturbance observer (ALDO) is first introduced, designed to accurately estimate the unknown nonlinear dynamics and time-varying disturbances within the system. This ALDO possesses online learning capabilities, enabling it to estimate the unknown upper bound of the disturbance derivative in real time, thus significantly reducing reliance on prior knowledge of the disturbance derivative and ensuring finite-time stability of the disturbance estimation error system. Furthermore, utilizing adaptive backstepping technology, a virtual controller is designed to compensate for mismatching disturbances within the closed-loop system. Additionally, a composite controller is developed to effectively compensate for disturbances and guarantee asymptotic convergence of the tracking control error to zero while maintaining signal boundedness within the system. Finally, the effectiveness and practicality of this control strategy are verified through a practical application case involving an electromechanical system. Note to Practitioners—This article investigates a class of nonlinear non-strict feedback systems affected by multi-disturbances, where the unknown nonlinear dynamics are functions of the full-state variable, rendering traditional adaptive methods inapplicable due to the potential for the algebraic loop problem. In complex engineering environments, where various external disturbances adversely impact system stability and performance, and prior knowledge of such disturbances is elusive, the disturbance observer-based composite control strategy explored in this paper stands out as crucial. The proposed strategy adeptly mitigates or eliminates disturbances via feedforward and feedback channels, enabling asymptotic tracking of the system while safeguarding its stable performance and reliability, holding promising applications in engineering domains like power systems, robot control, and traffic signal systems.