RESEARCH

Control by dynamic programming

We are often interested in practice in controlling a system such that its trajectories behave in the ``best'' way, we talk of optimal control. Examples include minimizing the fuel consumption of autonomous vehicles,  minimizing green house gaz emissions  in industrial applications etc. While simple analytical solutions are available since the 60's for plants modeled by finite-dimensional linear dynamical systems and for quadratic cost functions, no such explicit generic  solutions exist for general nonlinear dynamics and nonlinear cost functions. A powerful approach in this context is approximate dynamic programming (ADP), which provides near-optimal control inputs. ADP plays a key role in various domains such as optimal control obviously, reinforcement learning, and operational research.  

I investigate the interplay between (near-)optimality and stability for systems controlled by ADP and study how both can help each other.  My primary goal on this topic is to identify general conditions on systems controlled by ADP such that the closed-loop exhibits robust stability properties. Once stability is established, we can, in return, improve existing near-optimality bounds found in the ADP literature.  We then demonstrate in our works that stability can also be be exploited in the design of the optimization algorithm itself to reduce its computational complexity thus favoring its practical implementation.

Modeling, design and control of hybrid systems 

Hybrid dynamical systems exhibit both continuous-time and discrete-time dynamics. Examples include mechanical systems with impacts, power converters, networked control systems, sampled-data systems etc. 

My work in this field is twofold. I develop methodological tools adapted to networked control systems, as mentioned above. Recently, I also started investigating interconnected systems, which lead to hybrid systems. in the sense that each subsystem may be hybrid or the interconnection may lead to an overall hybrid system.  While power tools are now available to model and analyse the stability of stand-alone hybrid systems, the problem becomes quickly involved when interconnecting systems leading to hybrid systems. The challenge here is to develop modeling and analysis tools adapted to such systems. 

Nonlinear estimation and its application to electrochemical batteries

While efficient solutions exist since the 60's for the state estimation of finite-dimensional linear systems, the case of the non-linear systems is still unclear. Generic solutions exist for so-called uniformly observable systems, but these are not always easy to implement and suffer from major flaws in terms of robustness when it comes to practical implementation. 

My research activity consists in proposing state but also estimation methods for nonlinear systems, whose convergence is guaranteed analytically. Recently, I have been particularly interested by two aspects: the development of methodological hybrid techniques for estimation and the design of observers for electro-chemical batteries. The latter is done in close collaboration with SAFT company.

Networked control systems

Nowadays, controllers often communicate with the plant via a digital (wired or wireless) network, which may be used by other tasks: we talk of networked control systems (NCS). Examples include the remote control of mobile robots or platoons of vehicles exchanging information where a wireless network is used to ensure communications.  

This type of setups offers great advantages over classical point-to-point connections in terms of cost, flexibility, volume and ease of maintenance. On the other hand, the communication channel is not perfect in the sense that it induces errors on the transmitted signals, which  may have a major impact on the control performances. In this context, the challenge is to guarantee the desired properties for the closed-loop system despite the inevitable presence of communication constraints. 

My research activities on this topic mostly concentrate on nonlinear plant and controller models. A feature of my work is to model the overall closed-loop as a hybrid system, i.e. a dynamical system which exhibits both continuous-time dynamics, to describe the plant dynamics, and discrete-time dynamics, i.e. to represent transmissions over the network. 

I am particularly interested in event-triggered control, that is when transmission over the network are generated based on the current system needs, and not based on clocks. The underlying idea here is to use the network only when this is needed, in order to save communication ressources.