Indefinite LQ optimal control for discrete-time uncertain systems
Indefinite LQ optimal control for discrete-time uncertain systems
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DOI：
10.1007/s00500-019-04350-3
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发表时间：
2020-01
期刊：
影响因子：
4.1
通讯作者：
Yuefen Chen;Yuanguo Zhu
中科院分区：
文献类型：
--
作者：
Yuefen Chen;Yuanguo Zhu
研究离散时间不确定系统的线性二次最优控制问题，该系统的状态和控制权矩阵在代价函数中是不确定的。首先，利用Bellman最优性原理，得到离散不确定系统一般最优控制问题的递推式。然后，根据递归方程得到最优状态反馈控制。此外，给出了LQ问题的适定性充分条件，并给出了最优控制集的一般表达式。并利用所得结果给出了数值算例。最后，作为不确定LQ最优控制的一个应用，求解了不确定环境下的最优生产库存问题。
This paper is concerned with a linear quadratic (LQ) optimal control for discrete-time uncertain systems, with indefinite state and control weighting matrices in the cost function. Firstly, a recurrence equation of general optimal control problem for discrete-time uncertain systems is obtained by applying Bellman’s principle of optimality. Then, the optimal state feedback control is obtained based on the recurrence equation. Moreover, a sufficient condition of well-posedness for the LQ problem is proposed and a general expression for the optimal control set is given. Furthermore, a numerical example is presented by using the obtained results. Finally, as an application of the indefinite LQ optimal control, an optimal production inventory problem of uncertain environment is solved.