Optimal Control of Hybrid Systems with Regional Dynamics

Recently, hybrid control has become increasingly§relevant thanks to modern application domains§involving complex systems, sub-system§interconnections, mode-transitions, and heterogeneous§computational devices. Hybrid models, in which§continuous and discrete dynamics interact, have§proved useful for capturing these types of phenomena.§In this book, we consider hybrid systems with§regional dynamics where transitions between different§regimes occur as the state of the system crosses§given switching surfaces. In particular, we focus on§the associated optimal control problem and present a§hybrid Bellman equation that provides a§characterization of global optimality. The main§benefit of the proposed approach lies in the fact§that it presents both a theoretical representation of§the solution''s structure, and, from a more§application-driven point of view, a practical§algorithm that yields globally optimal solutions in a§regional dynamics framework. The recursive algorithm§is explored through numerous examples including a§heterogeneous multi-agent problem. The results should§be of interest to anyone working in: computer§science, control theory, system dynamics, and§operations research.