Abstract

We consider the problem of constructing reachable sets, i.e., sets of terminal states into which a system can be transferred from the origin in a fixed time, and 0-controllability sets, i.e., sets of initial states, from which a system can be transferred to the origin in a fixed time, for stationary linear discrete systems with a total control constraint. The representation of reachable and 0-controllable sets as linear transformations of superellipsoidal sets of finite and infinite dimensions is proved. A constructive method for describing the desired sets based on the apparatus of supporting half-planes is proposed, including for the limit sets of reachability and controllability. In the case of Euclidean spaces, the description is obtained explicitly. Examples are given. For a three-dimensional satellite motion control system in a near-circular orbit, reachability sets are modeled.

中文翻译：

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具有总控制约束的稳态线性离散系统有界可控性集的一些性质

摘要

我们考虑构造可达集（即系统可以在固定时间内从原点转移到的终止状态集）和0可控性集（即系统可以从其转移到的初始状态集）的问题对于具有总控制约束的平稳线性离散系统，在固定时间内回到原点。证明了可达集和0可控集作为有限维和无限维超椭球集的线性变换的表示。提出了一种基于半平面支撑装置的描述期望集合的构造方法，包括可达性和可控性的极限集合。在欧几里得空间的情况下，描述是明确获得的。给出了例子。针对近圆轨道上的三维卫星运动控制系统，对可达集进行建模。