Asymmetric-Constrained Nearly Optimal Tracking of Saturated Systems: Theory and Experiments

This article addresses the suboptimal high-precision tracking problem for a class of nonlinear systems, considering constraints on both state and input, by employing an asymmetric prescribed performance envelope. To make the equilibrium of the controlled plant coincide with its equivalent, a novel error transformation is proposed in this paper so that the equivalent tracking error can be mapped to an asymmetric prescribed boundary containing the origin. To address the optimal tracking control issue of the saturated nonlinear system with the non-zero equilibrium, a modified cost function corresponding to equivalent asymmetric state transformation is proposed, simplifying designing a saturated ADP error tracking controller. Since the equivalent system with asymmetric state constraints can be previously reduced to a logarithmic sliding-mode system, a fine-tracking precision is achieved by a high gain at the equilibrium while reducing the implementation difficulty of the proposed ADP controller. Experiments conducted on a permanent magnet synchronous motor (PMSM) system verify the effectiveness of the proposed control scheme.