Abstract

We consider optimal (on average) control problems and guaranteeing optimal control problems for bundles of trajectories of deterministic linear switchable systems such that the continuous variation of their state is described by differential equations, while the instant discrete changes of their state (switchings) are described by recurrent equations. The switching times and the number of switchings are not given. For one trajectory, the quality of the control is characterized by a quadratic functional taking into account the expenditure for each switching as well. Exact information about the initial state of the system is not known; therefore, control problems for bundles of trajectories are investigated. For linear-quadratic control problems for switching systems, the classical separation principle is not fulfilled. It turns out that its modification called the conditional separation principle holds. We provide academic examples of the synthesis of the optimal control on average and guaranteeing optimal control in which the separation principle is not fulfilled, while the conditional separation principle holds.

中文翻译：

---

确定性线性切换系统的轨迹控制问题中的分离定理

摘要

我们考虑最优（平均）控制问题，并为确定性线性可切换系统的轨迹束保证最优控制问题，以使它们的状态的连续变化通过微分方程来描述，同时描述其状态的瞬时离散变化（开关）通过循环方程式。没有给出切换时间和切换次数。对于一个轨迹，控制质量的特征是二次函数，同时考虑到每次切换的支出。有关系统初始状态的确切信息尚不清楚。因此，研究了轨迹束的控制问题。对于开关系统的线性二次控制问题，经典分离原理得不到满足。事实证明，它的修改被称为条件分离原理。我们提供了关于平均最优控制综合的学术实例，并保证了不满足分离原理而条件分离原理成立的最优控制。