Symbolic synthesis with average performance guarantees

We consider a general quantitative controller synthesis framework to synthesize controllers that not only enforce a desired input-output behavior on the closed-loop, but additionally minimize a certain average cost function, which is used to assess the closed loop behavior. We follow the usual symbolic synthesis approach, based on so-called discrete abstractions (also known as symbolic models) and propose a modification of the well-known system relations which enables the reasoning about the closed loop performance across related systems. We show how to construct symbolic models in terms of the newly introduced system relations for sampled-data, switched, nonlinear systems. A small numerical example is provided, to illustrate some of the theoretical results.