Stochastic Linear-Quadratic Optimal Control Problems with Markovian Regime Switching and $H_\infty$ Constraint under Partial Information
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918277887819776 |
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| author | Xiang, Na Shi, Jingtao |
| author_facet | Xiang, Na Shi, Jingtao |
| contents | This paper is concerned with a stochastic linear-quadratic optimal control problem of Markovian regime switching system with model uncertainty and partial information, where the information available to the control is based on a sub-$σ$-algebra of the filtration generated by the underlying Brownian motion and the Markov chain. Based on $H_\infty$ control theory, we turn to deal with a soft-constrained zero-sum linear-quadratic stochastic differential game with Markov chain and partial information. By virtue of the filtering technique, the Riccati equation approach, the method of orthogonal decomposition, and the completion-of-squares method, we obtain the closed-loop saddle point of the zero-sum game via the optimal feedback control-strategy pair. Subsequently, we prove that the corresponding outcome of the closed-loop saddle point satisfies the $H_\infty$ performance criterion. Finally, the obtained theoretical results are applied to a stock market investment problem to further illustrate the practical significance and effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04652 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Linear-Quadratic Optimal Control Problems with Markovian Regime Switching and $H_\infty$ Constraint under Partial Information Xiang, Na Shi, Jingtao Optimization and Control 93E20, 49N10, 60H10, 93B36, 93C41, 60J28, 91A15 This paper is concerned with a stochastic linear-quadratic optimal control problem of Markovian regime switching system with model uncertainty and partial information, where the information available to the control is based on a sub-$σ$-algebra of the filtration generated by the underlying Brownian motion and the Markov chain. Based on $H_\infty$ control theory, we turn to deal with a soft-constrained zero-sum linear-quadratic stochastic differential game with Markov chain and partial information. By virtue of the filtering technique, the Riccati equation approach, the method of orthogonal decomposition, and the completion-of-squares method, we obtain the closed-loop saddle point of the zero-sum game via the optimal feedback control-strategy pair. Subsequently, we prove that the corresponding outcome of the closed-loop saddle point satisfies the $H_\infty$ performance criterion. Finally, the obtained theoretical results are applied to a stock market investment problem to further illustrate the practical significance and effectiveness. |
| title | Stochastic Linear-Quadratic Optimal Control Problems with Markovian Regime Switching and $H_\infty$ Constraint under Partial Information |
| topic | Optimization and Control 93E20, 49N10, 60H10, 93B36, 93C41, 60J28, 91A15 |
| url | https://arxiv.org/abs/2601.04652 |