Bottom-Up Symbolic Control: Attractor-Based Planning and Behavior Synthesis

A class of hybrid systems with convergent continuous dynamics is abstracted to a special type of finite automata which operate on an infinite alphabet. The abstraction is predicate-based, enabled by the convergence properties of the continuous dynamics of the hybrid system, and encompasses existing low-level controllers rather than replacing them during synthesis. The abstract models are finite yet capable of storing and manipulating continuous data expressing attributes of the concrete hybrid model. The latter is shown to weakly simulate its discrete abstraction, and thus behaviors planned using the abstraction are always implementable on the concrete system. A case study illustrates how this methodology can be put into practice, orchestrating a temporal sequence of continuous controllers that allows the hybrid system to achieve a performance objective.