Receding Horizon Control-Based Stabilization of Singular Stochastic Systems with State Delay

doi:10.1007/s12204-022-2550-2

Abstract

Abstract: For a class of discrete-time singular stochastic systems with multi-state delay, the stabilization problem of receding horizon control (RHC) is concerned. Due to the difficulty in solving the proposed optimization problem, the RHC stabilization for such systems has not been solved. By adopting the forward and backward equation technique, the optimization problem is solved completely. A sufficient and necessary condition for the optimization controller to have a unique solution is given when the regularization and pulse-free conditions are satisfied. Based on this controller, an RHC stabilization condition is derived, which is in the form of linear matrix inequality. It is proved that the singular stochastic system with multi-state delay is stable in the mean-square sense under appropriate assumptions when the terminal weighting matrix satisfies the given inequality. Numerical examples show that the proposed RHC method is effective in stabilizing singular stochastic systems with multi-state delay.

Key words: receding horizon control (RHC), singular stochastic system, state delay, stabilization

摘要： 针对一类具有多重状态延迟的离散时间奇异随机系统，本研究关注滚动时域控制的稳定性问题。由于所提优化问题的求解难度较大，此类系统的滚动时域控制稳定性问题尚未得到解决。通过采用前向和后向方程技术，本研究完全解决了这一优化问题。在满足正则化和无脉冲条件下，给出了优化控制器具有唯一解的充分必要条件。基于这一控制器，推导出了滚动时域控制的稳定性条件，该条件以线性矩阵不等式的形式表示。证明了在适当假设下，当终端加权矩阵满足给定不等式时，具有多重状态延迟的奇异随机系统在均方意义下是稳定的。数值算例表明，所提滚动时域控制方法对于稳定具有多重状态延迟的奇异随机系统是有效的。

关键词: 滚动时域控制（RHC），奇异随机系统，状态时滞，稳定性

CLC Number:

TP273

WANG Xiaojing(王晓静),LIU Xiaohua(刘晓华), GAO Rong（高荣）. Receding Horizon Control-Based Stabilization of Singular Stochastic Systems with State Delay[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(3): 436-449.

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