无限阶双曲型系统的初始状态最优控制

A. Kowalewski
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引用次数: 2

摘要

文献[5]、[6]、[7]、[8]、[9]和[10]分别研究了与二阶时滞双曲型系统最优控制相关的各种优化问题。本文研究一类线性无限阶双曲型系统的最优控制问题。其中一个初始条件由控制函数给出。给出了具有Dirichlet边界条件的双曲型方程存在唯一解的充分条件。性能泛函具有二次型。时间范围T是固定的。最后,我们对控制施加一些约束。利用Lions方案([11]),导出了具有二次性能泛函和约束控制的Dirichlet问题的最优性的充分必要条件。
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Optimal control via initial state of an infinite order hyperbolic system
Various optimization problems associated with the optimal control of second order time delay hyperbolic systems have been studied in [5], [6], [7], [8], [9] and [10] respectively. In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the control. Making use of the Lions scheme ([11]), necessary and sufficient conditions of optimality for the Dirichlet problem with the quadratic performance functional and constrained control are derived.
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