A Design Framework for Hierarchical, Hybrid Control

Large scale systems are common in applications such as chemical process control, power generation and distribution and transportation systems, among others. Of particular interest are multi-agent, scarce resource problems, where a large number of agents have to make e cient use of a scarce resource. Here we try to approach the problem of large scale systems from a hierarchical, hybrid control view point. Our analysis is based on a new hybrid dynamical system formulation, that allows us to model large scale systems in a modular fashion. We primarily address the problem of controller design for multi-agent systems. A design procedure is proposed that naturally leads to hierarchical, hybrid control schemes, with continuous controllers trying to optimize each agent's resource utilization at a lower level and discrete controllers resolving inter-agent con icts at a higher level. An algorithm is presented to design the continuous controllers, as well as abstractions of their performance in terms of the discrete level. The algorithm makes use of ideas from game theory, treating the design process as a two player, zero sum game, between the controller of an agent and the disturbance generated by the actions of other agents. The resulting abstractions can be thought of as guidelines for the design of the discrete layer. If the resulting continuous controllers are used and the discrete controller satis es the guidelines, the closed loop hybrid system is, by design, guaranteed to exhibit the desired behavior. We demonstrate our algorithm by application to the automated vehicle following problem.