State‐input constrained asymptotic null‐controllability by a set‐valued approach

This study presents a unified approach to investigate asymptotic null‐controllability under possibly mixed constraints on state and control, for standard ordinary differential equation control systems. Using tools from set‐valued analysis and viability theory, initial data which can be steered to the origin at infinity are provided through a new type of Lyapunov functions. The corresponding controls are given via selections of adequately designed multifunctions, which are examined in both cases of convex constraints and the class of affine‐control systems. Finally, numerical examples from classical mechanics are given to verify the theoretical results.