Mathematics > Optimization and Control
[Submitted on 26 Jul 2023 (v1), last revised 3 Jan 2024 (this version, v4)]
Title:Robust Regret Optimal Control
View PDF HTML (experimental)Abstract:This paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete-time by an uncertain linear time-invariant (LTI) system. An optimal non-causal controller is constructed using the nominal plant model and given full knowledge of the disturbance. Robust regret is defined relative to the performance of this optimal non-causal control. It is shown that a controller achieves robust regret if and only if it satisfies a robust $H_\infty$ performance condition. DK-iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret. The approach is demonstrated three examples: (i) a simple single-input, single-output classical design, (ii) a longitudinal control for a simplified model for a Boeing 747 model, and (iii) an active suspension for a quarter car model. All examples compare the robust regret optimal against regret optimal controllers designed without uncertainty.
Submission history
From: Peter Seiler [view email][v1] Wed, 26 Jul 2023 16:56:36 UTC (1,036 KB)
[v2] Mon, 31 Jul 2023 13:52:30 UTC (1,036 KB)
[v3] Thu, 24 Aug 2023 16:04:19 UTC (1,036 KB)
[v4] Wed, 3 Jan 2024 20:11:49 UTC (1,590 KB)
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