## Section: New Results

### New results on Axis 2: Large Systems Models

#### Smart Transportation Systems

**Participants :** Nathalie Bertrand, Loïc Hélouët, Ocan Sankur

##### Smart regulation of urban train systems.

We have considered application of model checking techniques to evaluate performances of urban train systems [15]. Metros are subject to unexpected delays due to weather conditions, incidents, passenger misconduct, etc. To recover from delays and avoid their propagation to the whole network, metro operators use regulation algorithms that adapt speeds and departure dates of trains. Regulation algorithms are ad-hoc tools tuned to cope with characteristics of tracks, rolling stock, and passengers habits. However, there is no universal optimal regulation adapted in any environment. So, performance of a regulation must be evaluated before its integration in a network. In this work, we use probabilistic model-checking to evaluate the performance of regulation algorithms in simple metro lines. We model the moves of trains and random delays with Markov decision processes, and regulation as a controller that forces a decision depending on its partial knowledge of the state of the system. We then use the probabilistic model checker PRISM to evaluate performance of regulation: We compute the probability to reach a stable situation from an unstable one in less than d time units, letting d vary in a large enough time interval. This approach is applied on a case study, the metro network of Glasgow.

#### Supervisory Control

**Participants :** Hervé Marchand

##### Towards resilient supervisors against sensor deception attacks.

As a security problem, we considered in [24] feedback control systems where sensor readings may be compromised by a malicious attacker intent on causing damage to the system. We study this problem at the supervisory layer of the control system, using discrete event systems techniques. We assume that the attacker can edit the outputs from the sensors of the system before they reach the supervisory controller. In this context, we formulate the problem of synthesizing a supervisor that is robust against a large class of edit attacks on the sensor readings. The solution methodology is based on the solution of a partially observed supervisory control problem with arbitrary control patterns.

#### Multi-agent systems

**Participants :** Arthur Queffelec, Nicolas Markey, Ocan Sankur

##### Multi-agent path planning problems.

We are motivated by the increasing appeal of robots in information-gathering missions. In the problems we study [21], [22], the agents must remain interconnected. We model an area by a topological graph specifying the movement and the connectivity constraints of the agents. We study the theoretical complexity of the reachability and the coverage problems of a fleet of connected agents on various classes of topological graphs. We establish the complexity of these problems on known classes, and introduce a new class called sight-moveable graphs which admit efficient algorithms.

##### Quantitative semantics for Strategy Logic

We introduce and study SL[F], a quantitative extension of SL (Strategy Logic) [19], one of the most natural and expressive logics describing strategic behaviours. The satisfaction value of an SL[F] formula is a real value in [0,1], reflecting "how much" or "how well" the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of SL[F] in quantitative reasoning about multi-agent systems, by showing how it can express concepts of stability in multi-agent systems, and how it generalises some fuzzy temporal logics. We also provide a model-checking algorithm for our logic, based on a quantitative extension of Quantified CTL.