My research interests deal with analysis and control of hybrid systems with an emphasis on computational approaches, formal methods and applications to cyber-physical systems. I have made several contributions in the following domains:
Reachability analysis is a major research topic in hybrid systems with applications to algorithmic verification or controller synthesis. We worked on algorithms for computing over-approximations of the reachable set of continuous and hybrid systems. For systems with linear and affine continuous dynamics, we have proposed discretization schemes and developed several implementations using efficient algorithms and innovative data structures based on zonotopes and support functions. These techniques enabled a spectacular improvement of scalability with respect to existing approaches at the time. They form today the core of the verification platform SpaceEx.
Theories of system approximation are fundamental for the analysis and control of complex dynamical systems. We have proposed a framework for system approximation that extends the usual hierarchy of behavioral relationships given by language inclusion, simulation and bisimulation in a quantitative way using metrics. We introduced the notions of approximate simulation and bisimulation and established their characterization with Lyapunov-like functions called simulation and bisimulation functions. Unlike usual relationships, these notions are robust to unmodeled disturbances and are thus well suited to approximation of continuous and hybrid systems. Approximate bisimulation has been widely used in hybrid systems and has encountered many successful applications. Such applications include model reduction for continuous and hybrid systems as well as hierarchical control systems design or simulation-based verification.
The field of symbolic control is concerned with the use of algorithmic techniques for discrete controller synthesis for designing controllers for continuous dynamical systems. The key concept in symbolic control is that of symbolic model, which is a discrete dynamical system obtained by abstracting the trajectories of a continuous dynamical system over a finite set of symbols. We have shown how symbolic control could be recast in the approximate bisimulation framework leading to novel approaches for symbolic controller synthesis as well as new abstraction techniques for computing arbitrarily precise symbolic models of incrementally stable systems. Our most recent research efforts in the field of symbolic control have been devoted to the development of scalable and robust abstraction and controller synthesis techniques using multi-scale, compositional or quantitative approaches.
We also made contributions to several problems in the field of systems and control, outside the area of hybrid systems. We worked on multi-agent systems, designing consensus-based distributed algorithms for community detection in large networks, or proving very weak sufficient conditions for continuous-time consensus. We have introduced dynamic event-triggering mechanisms in the field of networked control systems. We have also made several contributions to analysis and control of hyperbolic partial differential equations such as singular perturbation approximations, or switching and event based stabilization.