Hybrid games are a powerful framework for modelling interactions between cyber-physical systems (CPS). While their high level of nondeterminism allows the modelling of complex systems, it also makes many properties undecidable. This paper presents Hybrid Games with Triggers (HGT), an extension that reduces nondeterminism by embedding agents' rational decision-making as triggers -conditions that, when met, prompt the agents to act. This approach leads to a time-abstract discrete game with a countable state space, where an agent has a winning strategy in the discrete game if and only if they do in the HGT. Our discretisation preserves both the continuous and discrete dynamics of the original hybrid game, providing a more structured, analysable model without sacrificing dynamic expressivity.

Semi-automated vehicles and driver assistance systems promise to increase aspects like traffic safety, more sustainable transportation systems and more road comfort. For a desirable future with the autonomous traffic agents (ATAs) that steer these automated mobility systems, it is of paramount importance to draw our attention to dynamic consistency management. A dynamic inconsistency is a run-time conflict, where an agent cannot choose an action without violating existing traffic rules or central safety goals. We suggest a step-wise engineering methodology to enable ATAs to cope with such run-time conflicts. For this, known run-time conflict must first be identified and formalised. We propose to sort similar conflicts into conflict clusters. For each conflict cluster, a conflict resolution strategy must be derived. Finally, we discuss explainability as a means to justify a conflict resolution strategy to involved stakeholders.

As automation increases qualitatively and quantitatively in safety-critical human cyber-physical systems, it is becoming more and more challenging to increase the probability or ensure that human operators still perceive key artifacts and comprehend their roles in the system. In the companion paper, we proposed an abstract reference architecture capable of expressing all classes of system-level interactions in human cyber-physical systems. Here we demonstrate how this reference architecture supports the analysis of levels of communication between agents and helps to identify the potential for misunderstandings and misconceptions. We then develop a metamodel for safe human machine interaction. Therefore, we ask what type of information exchange must be supported on what level so that humans and systems can cooperate as a team, what is the criticality of exchanged information, what are timing requirements for such interactions, and how can we communicate highly critical information in a limited time frame in spite of the many sources of a distorted perception. We highlight shared stumbling blocks and illustrate shared design principles, which rest on established ontologies specific to particular application classes. In order to overcome the partial opacity of internal states of agents, we anticipate a key role of virtual twins of both human and technical cooperation partners for designing a suitable communication.

The design and analysis of multi-agent human cyber-physical systems in safety-critical or industry-critical domains calls for an adequate semantic foundation capable of exhaustively and rigorously describing all emergent effects in the joint dynamic behavior of the agents that are relevant to their safety and well-behavior. We present such a semantic foundation. This framework extends beyond previous approaches by extending the agent-local dynamic state beyond state components under direct control of the agent and belief about other agents (as previously suggested for understanding cooperative as well as rational behavior) to agent-local evidence and belief about the overall cooperative, competitive, or coopetitive game structure. We argue that this extension is necessary for rigorously analyzing systems of human cyber-physical systems because humans are known to employ cognitive replacement models of system dynamics that are both non-stationary and potentially incongruent. These replacement models induce visible and potentially harmful effects on their joint emergent behavior and the interaction with cyber-physical system components.

We propose a reference architecture of safety-critical or industry-critical human cyber-physical systems (CPSs) capable of expressing essential classes of system-level interactions between CPS and humans relevant for the societal acceptance of such systems. To reach this quality gate, the expressivity of the model must go beyond classical viewpoints such as operational, functional, and architectural views and views used for safety and security analysis. The model does so by incorporating elements of such systems for mutual introspections in situational awareness, capabilities, and intentions to enable a synergetic, trusted relation in the interaction of humans and CPSs, which we see as a prerequisite for their societal acceptance. The reference architecture is represented as a metamodel incorporating conceptual and behavioral semantic aspects. We illustrate the key concepts of the metamodel with examples from cooperative autonomous driving, the operating room of the future, cockpit-tower interaction, and crisis management.