Adaptive Finite-Time Sliding Optimal Tracking Control for Uncertain Linear Systems With Disturbances

This paper proposes an adaptive finite-time sliding optimal tracking control (AFSOTC) for uncertain linear systems by combining finite-time optimal tracking with integral sliding mode technology. The AFSOTC includes two components: an optimal finite-time feedback control based on the finite-time control technique for a nominal model, and an integral finite-time sliding control to attenuate external disturbances. First, a sliding model is constructed to transform the tracking problem into a regular control one. The finite-time optimal controller based on the fixed-time stability technique and adaptive dynamic programming is proposed for the uncertain sliding model system, where an improved finite-time algebraic-Riccati-equation (ARE) with fixed-time convergence is online solved by a novel adaptive law. Then, an integral finite-time sliding control is constructed to resist the uncertain dynamics and interferences. Moreover, Lyapunov theory is applied to prove the parameter convergence and the stability of the closed-loop system with the AFSOTC. Finally, a linear system with comparisons and an autonomous underwater vehicle (AUV) with dynamic uncertainties and disturbance are applied to verify the correctness of the proposed method, and a linearization method for AUV underwater is presented. Note to Practitioners—Many linearized systems in practical engineering require finite-time optimal control to improve the tracking performance and also suffer from unknown disturbances, i.e., aerospace and navigation, F-16 aircraft, and autonomous vehicles. Moreover, the accurate models of these systems are generally difficult to construct because of dynamic uncertainties, such that the control performance will be reduced. The optimal finite-time control problem with disturbance and unknown dynamics for these systems is an open research challenge. Thus, this paper proposes an adaptive finite-time sliding optimal tracking control based on the sliding mode and fixed-time techniques, which can realize a fast optimal performance for uncertain linear systems with disturbances.