Biblio

Delayed coupling between state variables occurs regularly in technical dynamic systems, especially embedded control. As it consequently is omnipresent in safety-critical domains, there is an increasing interest in the safety verifications of systems modeled by Delay Differential Equations (DDEs). In this paper, we leverage qualitative guarantees for the existence of an exponentially decreasing estimation on the solutions to DDEs as established in classical stability theory, and present a quantitative method for constructing such delay-dependent estimations, thereby facilitating a reduction of the verification problem over an unbounded temporal horizon to a bounded one. Our technique builds on the linearization technique of non-linear dynamics and spectral analysis of the linearized counterparts. We show experimentally on a set of representative benchmarks from the literature that our technique indeed extends the scope of bounded verification techniques to unbounded verification tasks. Moreover our technique is easy to implement and can be combined with any automatic tool dedicated to bounded verification of DDEs.

In the future, mixed traffic Highly Automated Vehicles (HAV) will have to resolve interactions with human operated traffic. A particular problem for HAVs is the detection of human states influencing safety, critical decisions, and driving behavior of humans. We demonstrate the value proposition of neurophysiological sensors and driver models for optimizing performance of HAVs under safety constraints in mixed traffic applications.

We study conflict situations that dynamically arise in traffic scenarios, where different agents try to achieve their set of goals and have to decide on what to do based on their local perception.
We distinguish several types of conflicts for this setting. In order to enable modelling of conflict situations and the reasons for conflicts, we present a logical framework that adopts concepts from epistemic and modal logic, justification and temporal logic. Using this framework, we illustrate how conflicts can be identified and how we derive a chain of justifications leading to this conflict. We discuss how conflict resolution can be done when a vehicle has local, incomplete information, vehicle to vehicle communication (V2V) and partially ordered goals.

The possible interactions between a controller and its environment can naturally be modelled as the arena of a two-player game, and adding an appropriate winning condition permits to specify desirable behavior. The classical model here is the positional game, where both players can (fully or partially) observe the current position in the game graph, which in turn is indicative of their mutual current states. In practice, neither sensing or actuating the environment through physical devices nor data forwarding to and signal processing in the controller are instantaneous. The resultant delays force the controller to draw decisions before being aware of the recent history of a play. It is known that existence of a winning strategy for the controller in games with such delays is decidable over finite game graphs and with respect to ω-regular objectives. The underlying reduction, however, is impractical for non-trivial delays as it incurs a blow-up of the game graph which is exponential in the magnitude of the delay. For safety objectives, we propose a more practical incremental algorithm synthesizing a series of controllers handling increasing delays and reducing game-graph size in between. It is demonstrated using benchmark examples that even a simplistic explicit-state implementation of this algorithm outperforms state-of-the-art symbolic synthesis algorithms as soon as non-trivial delays have to be handled. We furthermore shed some light on the practically relevant case of non-order-preserving delays, as arising in actual networked control, thereby considerably extending the scope of regular game theory under delay pioneered by Klein and Zimmermann.