A Formal Framework for User-centric Control of Multi-Agent Cyber-physical Systems

Cyber physical systems are examples of a new emerging modelling paradigm that can be defined as multi-dimensional system coengineering (MScE). In MScE, different aspects of complex systems are considered altogether, producing emergent properties, or loosing some useful ones. This holistic approach requires interdisciplinary methods that result from formal mathematical and AI co-engineering. In this paper, we propose a formal framework consisting of a reference model for multi-agent cyber physical systems, and a formal logic for expressing safety properties. The agents we consider are enabled with continuous physical mobility and evolve in an uncertain physical environment. Moreover, the model is user centric, by defining a complex control that considers the output of a runtime verification process, and possible commands of a human controller. The formal logic, called safety analysis logic (SafAL), combines probabilities with epistemic operators. In SafAL, one can specify the reachability properties of one agent, as well as prescriptive commands to the user. We define symmetry reduction semantics and a new concept of bisimulation for agents. A full abstraction theorem is presented, and it is proved that SafAL represents a logical characterization of bisimulation. A foundational study is carried out for model checking SafAL formulae against Markov models. A fundamental result states that the bisimulation preserves the probabilities of the reachable state sets.