Control of Hybrid Systems using Qualitative Simulation

This paper presents a methodology for synthesizing, under uncertainty, a sequence of robust, discrete control actions to drive a continuous dynamical plant through admissible trajectories specified via temporal logic expressions . An action is defined as a modification to the value of a controllable exogenous variable . The TEQSIM algorithm combines qualitative simulation with temporal logic model checking to validate or refine a proposed plan . Qualitative simulation is used to infer a branching-time description of the system behaviors that potentially follow from a sequence of control actions . This description is queried using temporal logic based goal constraints to perform plan validation . Plan refinement infers bounds on the sequence of actions within a plan to guarantee that the specified goal constraints are satisfied . A framework for plan generation is presented that uses a phase portrait representation to reason about the effect of each action within a particular system configuration . This methodology is able to prune the plan search space by eliminating actions that are unable to resolve a detected goal violation .