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arXiv · 2604.04165

Input Matrix Optimization for Desired Reachable Set Warping of Linear Systems

Hrishav Das·Melkior Ornik
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Abstract

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.

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Hrishav Das, Melkior Ornik. 2026-04-05. Input Matrix Optimization for Desired Reachable Set Warping of Linear Systems. https://arxiv.org/abs/2604.04165

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