A Partial Order Approach to Discrete Dynamic Feedback in a Class of Hybrid Systems

We consider the dynamic feedback problem in a class of hybrid systems modeled as (infinite) state deterministic transition systems, in which the continuous variables are available for measurement. The contribution of the present paper is twofold. First, a novel framework for performing dynamic feedback is proposed which relies on partial orders on the sets of inputs and of discrete states. Within this framework, a state estimator updates a lower and an upper bound of the set of current states. A controller then uses such upper and lower bounds to compute the upper and lower bounds of the set of inputs that maintain the current state in a desired set. Second, we show that under dynamic controllability assumptions, the conditions that allow to apply the developed algorithms can always be verified. Therefore, the partial order approach to dynamic feedback is general. A multi-robot system is presented to show the computational advantages in a system in which the size of the state set can be so large as to render enumeration and exhaustive techniques inapplicable.