Abstract

This paper presents a robust version of the discrete-time minimum principle for uncertain systems. The uncertainty enters the dynamics of the system by an unknown value that belongs to a finite set. Each element of such a set represents a possible dynamic realization of the discrete-time trajectory. Following a mathematical programming approach, we reformulate the problem to obtain general necessary conditions that allow finding the worst-case optimality in the form of a weighted sum. These conditions are then applied to the time-varying linear affine quadratic problem with multiple modes and a general cost, which includes tracking signals in both: the state and the control variables. We illustrate our result with an application to a production-inventory control problem with uncertain dynamics.

摘要

本文介绍了不确定系统的离散时间最小原则的稳健版本。不确定性通过属于有限集的未知值进入系统的动态。这种集合的每个元素代表离散时间轨迹的可能动态实现。按照数学规划方法，我们重新制定问题以获得一般必要条件，从而允许以加权和的形式找到最坏情况的最优性。然后将这些条件应用于具有多种模式和一般成本的时变线性仿射二次问题，其中包括跟踪信号：状态和控制变量。我们通过对具有不确定动态的生产库存控制问题的应用来说明我们的结果。