An Invariant Based Approach to the Design of Hybrid Control Systems

In this paper, a methodology for hybrid control design is presented. The hybrid systems of interest are characterized by a feedback architecture of a continuous nonlinear plant with a discrete-event controller.The natural invariants of the continuous dynamics are used to partition the state space into regions and to synthesize simple and efficient control laws. The paper contains a complete description of the approach including a description of the hybrid control system modeling, of the invariant based approach for the design of the partition, and of the controller synthesis methodology illustrated by examples. The implementation and optimization of the approach are also discussed. The approach presented in this paper not only describes a viable methodology to hybrid design, but also addresses fundamental issues in hybrid system theory that arise in reachability analysis and verification approaches that are based on partitions of the continuous state space. Finally, the developed techniques are adapted and applied to digital control systems.