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.