Input Matrix Optimization for Desired Reachable Set Warping of Linear Systems
This addresses a fundamental challenge in control design for shaping reachable sets, with implications for performance and safety in applications like aerospace and mechanical systems, but it appears incremental as it builds on existing reachable set methods.
The paper tackles the problem of selecting an optimal input matrix for linear systems to maximize warping of the reachable set along a specific direction, reducing it to a finite number of linear optimization problems under certain assumptions and showing heuristic success when relaxed.
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.