Constrained control for uncertain linear systems
Constrained control for uncertain linear systems
复制标题
不确定线性系统的约束控制
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
F. Blanchini
中科院分区：
文献类型：
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作者：
F. Blanchini
研究了具有状态和控制约束的不确定线性系统的线性状态反馈综合问题。我们假设不确定性存在于状态矩阵和输入矩阵中，并且它们是有界的。主要目标是找到一个线性控制律，确保在每个时间都满足状态和输入约束。通过将状态限制在一个包含在允许状态区域中的紧凸正不变集内来解决该问题.证明了，如果控制、状态和不确定性都受线性不等式约束，且指定了一个紧凸多面体候选集，一个反馈矩阵，确保该区域是积极不变的封闭-对于连续时间和离散时间设计问题，回路系统都可以看作是一组线性不等式的解，这些结果被推广到存在附加干扰的情况。研究了正不变性与系统稳定性之间的关系，给出了多面体型正不变性区域存在的条件。
The linear state feedback synthesis problem for uncertain linear systems with state and control constraints is considered. We assume that the uncertainties are present in both the state and input matrices and they are bounded. The main goal is to find a linear control law assuring that both state and input constraints are fulfilled at each time. The problem is solved by confining the state within a compact and convex positively invariant set contained in the allowable state region.It is shown that, if the controls, the state, and the uncertainties are subject to linear inequality constraints and if a candidate compact and convex polyhedral set is assigned, a feedback matrix assuring that this region is positively invariant for the closed-loop system is found as a solution of a set of linear inequalities for both continuous and discrete time design problems.These results are extended to the case in which additive disturbances are present. The relationship between positive invariance and system stability is investigated and conditions for the existence of positively invariant regions of the polyhedral type are given.