Hands-Off Covariance Steering: Inducing Feedback Sparsity via Iteratively Reweighted $\ell_{1,p}$ Regularization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909784989499392 |
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| author | Kumagai, Naoya Oguri, Kenshiro |
| author_facet | Kumagai, Naoya Oguri, Kenshiro |
| contents | We consider the problem of optimally steering the state covariance matrix of a discrete-time linear stochastic system to a desired terminal covariance matrix, while inducing the control input to be zero over many time intervals. We propose to induce sparsity in the feedback gain matrices by using a sum-of-norms version of the iteratively reweighted $\ell_1$-norm minimization. We show that the lossless convexification property holds even with the regularization term. Numerical simulations show that the proposed method produces a Pareto front of transient cost and sparsity that is not achievable by a simple $\ell_1$-norm minimization and closely approximates the $\ell_0$-norm minimization obtained from brute-force search. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hands-Off Covariance Steering: Inducing Feedback Sparsity via Iteratively Reweighted $\ell_{1,p}$ Regularization Kumagai, Naoya Oguri, Kenshiro Optimization and Control We consider the problem of optimally steering the state covariance matrix of a discrete-time linear stochastic system to a desired terminal covariance matrix, while inducing the control input to be zero over many time intervals. We propose to induce sparsity in the feedback gain matrices by using a sum-of-norms version of the iteratively reweighted $\ell_1$-norm minimization. We show that the lossless convexification property holds even with the regularization term. Numerical simulations show that the proposed method produces a Pareto front of transient cost and sparsity that is not achievable by a simple $\ell_1$-norm minimization and closely approximates the $\ell_0$-norm minimization obtained from brute-force search. |
| title | Hands-Off Covariance Steering: Inducing Feedback Sparsity via Iteratively Reweighted $\ell_{1,p}$ Regularization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.00690 |