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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.17581 |
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| _version_ | 1866916449444954112 |
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| author | Hu, Yang Talebi, Shahriar Li, Na |
| author_facet | Hu, Yang Talebi, Shahriar Li, Na |
| contents | To address deviations from expected performance in stochastic systems, we propose a risk-sensitive control synthesis method to minimize certain risk measures over the limiting stationary distribution. Specifically, we extend Worst-case Conditional Value-at-Risk (W-CVaR) optimization for Linear Time-invariant (LTI) systems to handle nonzero-mean noise and affine controllers, using only the first and second moments of noise, which enhances robustness against model uncertainty. Highlighting the strong coupling between the linear and bias terms of the controller, we reformulate the synthesis problem as a Bilinear Matrix Inequality (BMI), and propose an alternating optimization algorithm with guaranteed convergence. Finally, we demonstrate the numerical performance of our approach in two representative settings, which shows that the proposed algorithm successfully synthesizes risk-sensitive controllers that outperform the naïve LQR baseline. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Risk-sensitive Affine Control Synthesis for Stationary LTI Systems Hu, Yang Talebi, Shahriar Li, Na Systems and Control To address deviations from expected performance in stochastic systems, we propose a risk-sensitive control synthesis method to minimize certain risk measures over the limiting stationary distribution. Specifically, we extend Worst-case Conditional Value-at-Risk (W-CVaR) optimization for Linear Time-invariant (LTI) systems to handle nonzero-mean noise and affine controllers, using only the first and second moments of noise, which enhances robustness against model uncertainty. Highlighting the strong coupling between the linear and bias terms of the controller, we reformulate the synthesis problem as a Bilinear Matrix Inequality (BMI), and propose an alternating optimization algorithm with guaranteed convergence. Finally, we demonstrate the numerical performance of our approach in two representative settings, which shows that the proposed algorithm successfully synthesizes risk-sensitive controllers that outperform the naïve LQR baseline. |
| title | Risk-sensitive Affine Control Synthesis for Stationary LTI Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.17581 |