Robust Regret Optimal Control
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915433593962496 |
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| author | Liu, Jietian Seiler, Peter |
| author_facet | Liu, Jietian Seiler, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14297 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robust Regret Optimal Control Liu, Jietian Seiler, Peter Optimization and Control Systems and Control 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. |
| title | Robust Regret Optimal Control |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2307.14297 |