Optimal control of partitioned hybrid systems via discrete-time Hamilton–Jacobi theory

Computational framework for optimal control of hybrid systems with a partitioned state space is presented. It is shown that necessary conditions for optimality for a discrete-time dynamic system can be solved concurrently for various boundary conditions, according to the recent development of discrete-time Hamilton–Jacobi theory. This unique property is utilized to construct computationally efficient numerical optimization of hybrid systems where discrete switching dynamics occurs at the boundary between partitions of the configuration space. A benchmark example shows that the proposed approach has substantial computational advantages compared with the existing ones.