Technical systems interacting with the real world can be ele- gantly modelled using probabilistic hybrid automata (PHA). Parametric probabilistic hybrid automata are dynamical systems featuring hybrid discrete-continuous dynamics and parametric probabilistic branching, thereby generalizing PHA by capturing a family of PHA within a sin- gle model. Such system models have a broad range of applications, from control systems over network protocols to biological components. We present a novel method to synthesize parameter instances (if such exist) of PHA satisfying a multi-objective bounded horizon specifica- tion over expected rewards. Our approach combines three techniques: statistical model checking of model instantiations, a symbolic version of importance sampling to handle the parametric dependence, and SAT- modulo-theory solving for finding feasible parameter instances in a multi- objective setting. The method provides statistical guarantees on the synthesized parameter instances. To illustrate the practical feasibility of the approach, we present experiments showing the potential benefit of the scheme compared to a naive parameter exploration approach.
['Martin Fränzle', 'Sebastian Gerwinn', 'Paul Kröger', 'Alessandro Abate', 'Joost-Pieter Katoen']
Multi-objective Parameter Synthesis in Probabilistic Hybrid Systems