Low-Complexity Switching Controllers for Safety Using Symbolic Models

In this paper, we consider the problem of synthesizing low-complexity safety controllers for incrementally stable switched systems. For that purpose, we establish a new approximation result for the computation of symbolic models that are approximately bisimilar to a given switched system. The main advantage over existing results is that it allows us to design quantized switching controllers for safety specifications; these can be computed offline and therefore the online execution time is greatly reduced. Then, we present a technique to reduce the memory needed to store the control law by borrowing ideas from algebraic decision diagrams for compact function representation and by exploiting the non-determinism inherent to safety controllers. We show the merits of our approach by applying it to a simple model of temperature regulation in a building.