On the Existence of Admissible Positional Controls for Systems with Mixed Constraints

Control systems with geometric constraints and both equality- and inequality-type constraints are considered. For these systems, we study the question of the existence of admissible positional controls in the class of continuous functions. We obtain sufficient conditions for the existence of local and global continuous admissible positional controls. For systems with smooth constraints, these sufficient conditions are formulated in terms of first-order derivative of mappings that define mixed constraints. For systems with Lipschitz constraints, sufficient conditions for the existence of admissible controls are formulated in terms of the Clarke’s generalized Jacobian of the mappings that define mixed constraints.