Abstract

The purpose of this paper is to discuss, by the use of the Balakrishnan’s epsilon method, a class of optimal control problems governed by continuous linear time invariant singular systems which have only a finite dynamic mode. The linear differential algebraic equation is handled using the epsilon technique to obtain a sequence of the calculus of variations problems. A convergence theorem is given to obtain approximate and, in the limit, an optimal solution of this class of optimal control problem by the use of the necessary optimality conditions of Euler–Lagrange type. A correspondence has been also shown between this penalty function and duality for this class of optimal control problems considered. As an application, an example of optimal linear quadratic problem is also given.

中文翻译：

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一类由Balakrishnan方法控制的最优控制问题

摘要

本文的目的是通过使用Balakrishnan的epsilon方法来讨论一类由连续线性时不变奇异系统控制的最优控制问题，该系统只有有限的动态模式。线性微分代数方程使用epsilon技术进行处理，以获得变化问题演算的序列。通过使用Euler–Lagrange类型的必要最优性条件，给出了一个收敛定理，以求得此类最优控制问题的近似值，并在极限情况下获得了最优解。对于这类考虑的最优控制问题，还显示了惩罚函数和对偶性之间的对应关系。作为应用，还给出了一个最佳线性二次问题的例子。