M.d.R. de Pinho , M. Margarida A. Ferreira , Georgi Smirnov
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引用次数: 0
摘要
在本文中,我们使用惩罚函数的方法来推导有状态约束问题的最优性必要条件,这种方法与我们之前用于解决控制扫掠过程优化问题的方法类似(参见 de Pinho 等人,2022 年)。我们的目的是提供一个最大原则的证明,让那些具有经典最优控制和基本函数分析基础知识的人也能轻松掌握。我们有意考虑平稳情况和最简单的边界条件;我们考虑全局最小值,并假设控制系统的轨迹集是紧凑的。
Optimal control problem with state constraints via penalty functions
In this paper, we derive necessary conditions of optimality for problems with state constraints using the method of penalty functions similar to the one we previously used to solve optimization problems for control sweeping processes (see, e.g., de Pinho et al., 2022). Our aim is to provide a proof of the Maximum Principle that can be easily followed by those with basic knowledge of classical optimal control and elementary functional analysis. We intentionally consider a smooth case and the simplest boundary conditions; we consider global minimum and assume that the set of trajectories of the control system is compact.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.