具有不同控制约束的线性控制系统可达集的近似计算

IF 0.3 Q4 MATHEMATICS
I. Zykov
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引用次数: 0

摘要

研究了当控制作用同时受到几何约束和若干积分约束时,线性控制系统可达性集的近似构造问题。本文提出了一种由连续系统过渡到离散系统的方法,即对时间间隔进行均匀划分,并在将其与平均值划分的步骤中替换控制。证明了当离散化步长趋于零时,逼近系统的可达集在Hausdorff度量中收敛于原系统的可达集,并给出了收敛速率的估计。在求解一类二次规划问题的基础上,提出了一种构造可达集边界的算法。并进行了数值模拟。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximate calculation of reachable sets for linear control systems with different control constraints
The paper considers the problem of approximate construction of reachability sets for a linear control system, when the control action is constrained simultaneously by geometric and several integral constraints. A variant of the transition from a continuous to a discrete system is proposed by uniformly dividing the time interval and replacing the controls at the step of dividing them with their mean values. The convergence of the reachability set of the approximating system to the reachability set of the original system in the Hausdorff metric is proved as the discretization step tends to zero, and an estimate is obtained for the rate of convergence. An algorithm for constructing the boundary of reachable sets based on solving a family of conic programming problems is proposed. Numerical simulation has been carried out.
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