On Design of Robust Linear Quadratic Regulators
On Design of Robust Linear Quadratic Regulators
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DOI：
10.23919/acc55779.2023.10156654
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发表时间：
2023-05
期刊：
影响因子：
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通讯作者：
Arash Komaee
中科院分区：
文献类型：
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作者：
Arash Komaee
研究了用线性二次型调节器（LQR）实现状态反馈的不确定线性系统的闭环稳定性。首先针对不反映系统不确定性的标称模型设计的非鲁棒LQR，给出了在存在不确定性时保证闭环稳定性的充分条件。由于这些条件通常在较大的不确定性下被违反，因此本文提供了一种方法将这种非鲁棒LQR重新设计为鲁棒LQR，以确保在预定义的不确定性水平下闭环稳定。本文的分析在很大程度上依赖于逆最优控制的概念来构造适合的不确定线性系统的性能度量，这些系统的结构是非二次型的，但产生LQR形式的最优控制。建立了鲁棒LQR与零和线性二次动态对策之间的关系。
Closed-loop stability of uncertain linear systems is studied under the state feedback realized by a linear quadratic regulator (LQR). Sufficient conditions are presented that ensure the closed-loop stability in the presence of uncertainty, initially for the case of a non-robust LQR designed for a nominal model not reflecting the system uncertainty. Since these conditions are usually violated for a large uncertainty, a procedure is offered to redesign such a non-robust LQR into a robust one that ensures closed-loop stability under a predefined level of uncertainty. The analysis of this paper largely relies on the concept of inverse optimal control to construct suitable performance measures for uncertain linear systems, which are non-quadratic in structure but yield optimal controls in the form of LQR. The relationship between robust LQR and zero-sum linear quadratic dynamic games is established.