A Nonsmooth Calculus for Solving Some Graph-Theoretic Control Problems*

Abstract: Motivated by the needs of real-time tasking of a nonlinear controlled dynamical system, we develop the notion of a real-valued label space to represent a complete graph. A walk in the graph maps to a controlled trajectory in label space. We use the indicator function as our primary tool to formulate such problems within a calculus-based setting. Urysohn’s Lemma forms the key bridge for approximating the resulting nonsmooth optimal control problem to a smooth computational framework. An illustrative uninhabited-aerial-vehicle collection planning and and scheduling problem is solved to illustrate the viability of the entire framework.