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针对高超声速飞行器非线性、多约束、快时变等特点,提出了一种基于线性矩阵不等式的滑模预测控制方法。首先设计系统的滑模面,然后对滑模面进行预测并将其作为优化性能指标,通过Schur补引理将控制律的设计转化为一个优化问题。该方法避免了常规滑模控制的高频切换,有效地克服了抖振现象。此外,相对于传统的滑模预测控制方法,该方法不需要额外计算终端约束条件和终端代价函数,只需要通过选取合适的李雅普诺夫函数即可保证系统的稳定性,且其加权矩阵是和控制律同时进行优化设计的,简化了设计过程。仿真试验表明,相比于单纯的预测控制和滑模控制,所提出的方法具有更好的跟踪性能。
Aiming at the characteristics of hypersonic aircraft such as nonlinearity, multiple constraints and fast time-varying, a sliding mode predictive control method based on linear matrix inequality (LMI) is proposed. Firstly, the sliding surface of the system is designed, and then the sliding surface is predicted and used as an optimal performance index. The control law design is transformed into an optimization problem by Schur complement theory. The method avoids the high frequency switching of the conventional sliding mode control and effectively overcomes the chattering phenomenon. In addition, compared with the traditional sliding mode predictive control method, this method does not need additional calculation of terminal constraints and terminal cost functions, and only needs to ensure the stability of the system by selecting the appropriate Lyapunov function. The weight matrix is The control law optimizes the design at the same time, simplifying the design process. Simulation results show that the proposed method has better tracking performance than simple predictive control and sliding mode control.