## Section: New Results

### Control of quantitative systems

#### Smart regulation for urban trains

Participants : Éric Fabre, Loïc Hélouët, Hervé Marchand, Abd El Karim Kecir.

The regulation of subway lines consists in accomodating small random perturbations in transit times as well as more impacting incidents, by playing on continuous commands (transit times and dwell times) and by making more complex decisions (insertions or extractions of trains, changes of missions, overpassing, shorter returns, etc.). The objectives are multiple : ensuring the regularity and punctuality of trains, adapting to transportation demand, minimizing energy consumption, etc. We have developed an event-based control strategy that aims at equalizing headways on a line. This distributed control strategy is remarquably robust to perturbations and reactive enough to accomodate train insertions/extractions. We have also developed another approach based on event graphs in order to optimally interleave trains at a junction.

#### Games and reactive synthesis

Participant : Ocan Sankur.

In game theory, a strategy is *dominated* by another one if the latter systematically yields a payoff as good as the former,
while also yielding a better payoff in some cases. A strategy is *admissible* if it is not dominated.
This notion is well studied in game theory and is useful to describe the set of strategies that are “reasonable” whose choice can be justified.
Recent works studied this notion in graph games with omega-regular objectives and investigated its applications in controller synthesis.
For multi-agent controller synthesis, admissibility can be used as a hypothesis on the behaviors of each agent, thus enabling a compositional
reasoning framework for controller synthesis. In [29], we investigate this framework for quantitative graph games.
We characterize admissible strategies, study their existence, and give an effective characterization of the set of paths that are compatible with
admissible payoffs. This is then used to derive algorithms for model checking under admissibility, but also assume-admissible synthesis.

In [21], we present the reactive synthesis competition (SYNTCOMP), a long-term effort intended to stimulate and guide advances in the design and application of synthesis procedures for reactive systems. The first iteration of SYNTCOMP is based on the controller synthesis problem for finite-state systems and safety specifications. We provide an overview of this problem and existing approaches to solve it, and report on the design and results of the first SYNTCOMP. This includes the definition of the benchmark format, the collection of benchmarks, the rules of the competition, and the five synthesis tools that participated. We present and analyze the results of the competition and draw conclusions on the state of the art. Finally, we give an outlook on future directions of SYNTCOMP.

In the invited [22], we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They include the assume-admissible synthesis on Boolean games, synthesis under multiple environments for Markov decision processes, and multi-objective synthesis with probability thresholds for Markov decision processes with multi-dimensional weights. They are part of the contributions obtained in the inVEST project funded by the European Research Council.

#### Runtime enforcement

Participants : Hervé Marchand, Thierry Jéron.

In the [20] we generalize our line of work on runtime enforcement for timed properties. Runtime enforcement is a verification/validation technique aiming at correcting possibly incorrect executions of a system of interest. In this work we consider enforcement monitoring for systems where the physical time elapsing between actions matters. Executions are thus modelled as timed words (i.e., sequences of actions with dates). We consider runtime enforcement for timed specifications modelled as timed automata. Our enforcement mechanisms have the power of both delaying events to match timing constraints, and suppressing events when no delaying is appropriate, thus possibly allowing for longer executions. To ease their design and their correctness-proof, enforcement mechanisms are described at several levels: enforcement functions that specify the input-output behaviour in terms of transformations of timed words, constraints that should be satisfied by such functions, enforcement monitors that describe the operational behaviour of enforcement functions, and enforcement algorithms that describe the implementation of enforcement monitors.

This year we went one step ahead [33] and consider predictive runtime enforcement, where the system is not entirely black-box, but we know something about its behavior. This *a priori* knowledge about the system allows to output some events immediately, instead of delaying them until more events are observed, or even blocking them permanently. This in turn results in better enforcement policies. We also show that if we have no knowledge about the system, then the proposed enforcement mechanism reduces to a classical non-predictive runtime enforcement framework. All our results are formalized and proved in the Isabelle theorem prover.

#### Decentralized control

Participant : Hervé Marchand.

In collaboration with Laurie Ricker, we have been interested in decentralized control of discrete event systems. In decentralized discrete-event system (DES) architectures, agents fuse their local decisions to arrive at the global decision. The contribution of each agent to the final decision is never assessed; however, it may be the case that only a subset of agents, i.e., a (static) coalition, perpetually contribute towards the correct final decisions. In casting the decentralized DES control (with and without communication) problem as a cooperative game, it is possible to quantify the average contribution that each agent makes towards synthesizing the overall correct control strategy. Specifically, we explore allocations that assess contributions of non-communicating and communicating controllers for this class of problems. This allows a quantification of the contribution that each agent makes to the coalition with respect to decisions made solely based on its partial observations and decisions made based on messages sent to another agent(s) to facilitate a correct control decision [34].