In this paper, optimal control problems governed by linear discrete-time descriptor noncausal systems (with quadratic input variables) are investigated in order. A descriptor system assumed to be regular alone is called descriptor noncausal system. According to Bellman's principle of optimality in dynamic programming, a recurrence equation for simplifying the optimal control problems is derived. Then, employing the recurrence equation, a bang-bang optimal control problem subject to a linear descriptor noncausal system and an optimal control problem subject to a descriptor noncausal system with quadratic input variables are both settled, and the optimal solutions are given through exact expressions. A numerical example is presented to illustrate the effectiveness of the results obtained concerning the bang-bang optimal control problem.

中文翻译：

---

离散时间描述符非因果系统的最优控制

在本文中，按顺序研究了由线性离散时间描述符非因果系统（具有二次输入变量）控制的最优控制问题。假设单独是正则的描述符系统称为描述符非因果系统。根据动态规划中的贝尔曼最优性原理，推导出了一个简化最优控制问题的递推方程。然后，利用递推方程求解线性描述符非因果系统下的bang-bang最优控制问题和具有二次输入变量的描述符非因果系统下的最优控制问题，并通过精确表达式给出最优解。给出了一个数值例子来说明所获得的关于 bang-bang 最优控制问题的结果的有效性。