Quantified Mu-calculus for Control Synthesis

We consider an extension of the mu-calculus as a general framework to describe and synthesize controllers. This extension is obtained by quantifying atomic propositions, we call the resulting logic quantified mu-calculus. We study its main theoretical properties and show its adequacy to control applications. The proposed framework is expressive : it offers a uniform way to describe as varied parameters as the kind of systems (closed or open), the control objective, the type of interaction between the controller and the system, the optimality criteria (fairness, maximally permissive), etc. To our knowledge, none of the former approaches can capture such a wide range of concept