Controllability of induced bilinear systems on the sphere

2025/06/09 by Marco A. Colque-Choquecallata, Colque-Choquecallata, Marco A., Efrain Cruz-Mullisaca +3
Engineering · #Adaptive Control of Nonlinear Systems #Control and Dynamics of Mobile Robots #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.07749

openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the controllability of bilinear control systems of the form s = As + uBs, where s ∈ \mathbbS² and A, B ∈ gl(3, ℝ) are skew-symmetric matrices. First, we prove that the algebraic condition [A, B] ≠ 0 ensures that the Lie algebra rank condition is satisfied for these systems. Next, we show that this same condition implies the controllability of the system. Finally, in an explicit and descriptive manner, we demonstrate controllability by exhibiting trajectories that transfer a given initial state to another.

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