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Abstract. Hybrid control systems contain two distinct types of systems, continuous state and discrete-state, that interact with each other. Their study is essential in designing sequential supervisory controllers for continuous-state systems, and it is central in designing control systems with high degree of autonomy. After an introduction to intelligent autonomous control and its relation to hybrid control, models for the plant, controller, and interface axe introduced. The interface contains memoryless mappings between the supervisor's symbolic domain and the plant's nonsymbolic state space. The simplicity and generality afforded by the assumed interface allows us to directly confront important system theoretic issues in the design of supervisory control systems, such as determinism, quasideterminism, and the relationship of hybrid system theory to the more mature theory of logical discrete event systems.

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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.

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