In this research area, we are interested in various aspects of the control and stabilisation or stability of solutions to partial differential equations. To be more precise:

• Control of partial differential equations
• Fluid-Structure Interaction
• Hamiltonian systems with interaction ports (pHS)

The idea behind interaction port Hamiltonian systems is to describe the dynamics of a system using the physical energy of the system (called the Hamiltonian).

In particular, this makes it possible to deal with non-linearities (non-quadratic Hamiltonian) in general. Analysis of the associated Cauchy problem is still an active research topic in the case of infinite-dimensional systems (typically non-linear partial differential equations).

Interaction ports classically consist of co-located control and observation (among other things), enabling different pHs to be coupled. The resulting system is still a pH. There are algebraic structures subordinate to pHs: Dirac structures.

Numerical simulation of pHs calls for special numerical methods to preserve the Hamiltonian (or, more precisely, the existence of a Dirac structure associated with the discretized system).

It should also be noted that closed-loop stabilisation is easily obtained in pHs, and that they also allow, at least in finite dimension, constraints to be taken into account in the form of algebraic equations coupled to the dynamical system.

• Fractional and Diffusive Differential Systems (SDF)
• Well-Posed Linear Systems (WPLS)

This area of research focuses on numerical optimisation and multidisciplinary optimisation in the context of pre-project design. To be more precise:

• Development and analysis of optimization algorithms (deterministic and stochastic)
• Solving large linear systems and preconditioning
• Uncertainty propagation (UQ)
• Sensitivity analysis
• Substitution models
• High-Performance Computing (HPC)

This area of research focuses on the application of probability and statistics to practical problems encountered by industry. To be more precise:

• Performance analysis of communication networks
• Sensitivity analysis
• Random trees

The Formal Methods and Dedicated Languages theme is concerned with the formal semantics of programming languages as well as programs and their specifications, applied particularly to languages adapted to the design of critical embedded systems.

The use of formal methods (programme proofs, SAT/SMT methods, correction by construction, etc.) for the rigorous design of avionics functions can be applied to the various stages in the design and implementation of a product: architecture consistency verification, proof of correct operation of model transformation/code generation tools, and proof of correctness of the application code to be embedded.

The study of dedicated languages (synchronous reactive, probabilistic, etc.) and their semantic aspects will ensure that programmes can be embedded for the implementation of avionics functions, for example, taking into account the strong requirements and constraints of the field, both in terms of computing resources and the implementation of advanced AI-based functions (neural networks or learning by Bayesian inference).

The Architecture and Simulation of Cyber-Physical Systems theme focuses on the V&V stages of critical systems, particularly in conjunction with the PRISE platform.

• New avionics architectures: taking into account new processor and network paradigms and their safe integration into an avionics platform (SMARTIES project)
• Embeddability of applications on hybrid architectures (CPU, GPU and FPGA), in particular neural networks and their complex decision tasks
• Systems simulation based on state-of-the-art tools
  • Real-time distributed simulation, through the implementation of the HLA standard by the CERTI middleware developed in partnership with ONERA. CERTI implements versions 1.3 and 1516 of the HLA simulation standard.
  • Interoperability and coupling of simulation models for cyber-physical systems, with the Ptolemy-HLA tool. This distributed co-simulation environment couples two open-source tools, Ptolemy II and CERTI/HLA. It takes advantage of Ptolemy's calculation models and the HLA standard for interoperability and deterministic distribution of simulations.