Convex dynamic programming for hybrid systems

A classical linear programming approach to optimization of flow or transportation in a discrete graph is extended to hybrid systems. The problem is finite dimensional if the state space is discrete and finite, but becomes infinite dimensional for a continuous or hybrid state space. It is shown how strict lower bounds on the optimal loss function can be computed by gridding the continuous state space and restricting the linear program to a finite-dimensional subspace. Upper bounds can be obtained by evaluation of the corresponding control laws.