Closed-Loop Dynamics Modeling and Knowledge-Based Control of Fractional-Order Systems With Output Constraints via Deterministic Learning.

Abstract

This article addresses the problem of closed-loop dynamics learning and tracking control for a class of fractional-order (FO) nonlinear strict-feedback systems subject to output constraints. To cope with the inherent nonlinear uncertainties, an adaptive FO learning control strategy is developed based on deterministic learning (DL) theory. A notable feature of the proposed method lies in its ability to accurately learn the uncertain nonlinear dynamics of the system during real-time closed-loop tracking control while ensuring both stability and convergence of the overall system. To mitigate the complexity explosion typically encountered in traditional backstepping designs due to virtual control laws, an improved adaptive FO filter is introduced. Subsequently, by incorporating the DL framework, an adaptive output-constrained control scheme is formulated using radial basis function neural networks (RBFNNs), enabling locally precise approximation of the nonlinear closed-loop dynamics while strictly satisfying the output constraints. Rigorous Lyapunov-based stability analysis demonstrates that: 1) the output of the FO system remains strictly within the prescribed constraint boundaries and achieves stable tracking of the desired reference trajectory and 2) the resulting linear time-varying (LTV) FO closed-loop system achieves exponential stability under persistent excitation (PE). This guarantees that the RBFNNs can achieve locally accurate identification of the dominant uncertain dynamics and preserve the acquired knowledge in the form of constant RBFNNs. Based on these results, an experience-based control scheme is further proposed, which leverages the previously learned dynamic knowledge to enhance control performance and reduce computational overhead while maintaining provable closed-loop stability.