Input Matrix Optimization for Desired Reachable Set Warping of Linear Systems
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911568491446272 |
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| author | Das, Hrishav Ornik, Melkior |
| author_facet | Das, Hrishav Ornik, Melkior |
| contents | Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear system that maximizes warping of the reachable set along a direction of interest. The main result establishes that under certain assumptions on the dynamics, the problem reduces to a finite number of linear optimization problems. When these assumptions are relaxed, we show heuristically that the same approach yields good results. The results are validated on two systems: a linearized ADMIRE fighter jet model and a damped oscillator with complex eigenvalues. The paper concludes with a discussion of future directions for reachable set warping research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04165 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Input Matrix Optimization for Desired Reachable Set Warping of Linear Systems Das, Hrishav Ornik, Melkior Systems and Control Optimization and Control Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear system that maximizes warping of the reachable set along a direction of interest. The main result establishes that under certain assumptions on the dynamics, the problem reduces to a finite number of linear optimization problems. When these assumptions are relaxed, we show heuristically that the same approach yields good results. The results are validated on two systems: a linearized ADMIRE fighter jet model and a damped oscillator with complex eigenvalues. The paper concludes with a discussion of future directions for reachable set warping research. |
| title | Input Matrix Optimization for Desired Reachable Set Warping of Linear Systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2604.04165 |