Discrete-time optimal feedback control via Hamilton-Jacobi theory with an application to hybrid systems

A computational framework for discrete-time optimal feedback control is presented. It is shown that discrete-time necessary conditions for optimality can be uniformly solved for varying boundary conditions, via the recent development of discrete-time Hamilton-Jacobi theory. This is extended to develop computational optimal feedback controls for hybrid systems with a partitioned state space, where discrete switching dynamics occur at the boundary between partitions of the configuration space. The desirable computational properties are illustrated by a numerical example.