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

초록

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. Note to Practitioners-Learning-based or approximate optimal control is widely studied due to its superior robustness. A large number of existing theoretical studies require the controlled system to be "square", so that optimal methods such as ADP can be deployed, which limits the application of such methods in second-order motion control systems like servo motors and robots. In addition, for an ideal nonlinear system, the zero equilibrium condition must be guaranteed such that the stability of a closed-loop system can be proved theoretically, but it is also usually difficult to be strictly guaranteed for engineering practices. Also, how to reasonably constrain the system convergence dynamics is also an interesting problem. This paper aims to provide insightful ideas for enhancing the existing solutions to the aforementioned problems: a sliding-mode function is proposed to reduce the order of the controlled system, so that it becomes a "square" one; a novel asymmetric prescribed performance mapping mechanism is constructed to constrain states; then, a modified cost function is employed to address the optimal tracking control issue of the saturated nonlinear system with the non-zero equilibrium. The proposed control scheme ensures that the motor can operate stably under load disturbances. Theoretical analysis and comparative experiments with state-of-the-art methods also confirm its effectiveness.

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