Ph. D. Project
Control of interconnected systems by dynamic programming: stability and robustness guarantees
2023/10/10 - 2026/10/09
This thesis is placed in the general framework of the development of intelligent networked autonomous
systems. Numerous fields of application today give rise to networks of dynamic systems, such as fleets of
drones or vehicles and energy networks. To allow the full development of these technologies, it is essential to
have at one's disposal adapted control methods that bring guarantees of stability and robustness as well as
performance (optimality).

In this context, the objective of this international thesis is to contribute to the development of methodological
tools for the synthesis of efficient, stabilizing and robust control laws for general nonlinear interconnected
systems. To this end, we will focus on dynamic programming techniques. Dynamic programming is the
preferred approach for constructing high-performance ("near-optimal") controllers for general systems and
cost functions, which is essential for complex networked systems when a model of the dynamics is available.
On the other hand, the controllers obtained by dynamic programming are not a priori endowed with stability
and robustness guarantees, which are essential in most applications of automation.

The goal of this thesis is therefore to identify conditions, or even to revisit dynamic programming algorithms,
in order to provide both performance and robust stability guarantees.

The main steps of the thesis will be the following: (i) establish input-output stability properties, intimately
related to robustness issues and essential for the implementation of distributed control laws later on, for an
isolated system; (ii) exploit these results for networks of systems initially when each agent of the network
must minimize a local cost; (iii) to develop versions of these control strategies based on data (and no longer
on a model of the dynamics), we speak here of reinforcement learning, to improve the autonomy of the
systems by directly synthesizing the control inputs from the available input-output data.

This PhD will be co-advised by Dragan Nesic from the University of Melbourne (Australia). One or several long
visit in Melbourne will be planned.
Dynamic programming, Lyapunov stability, interconnected systems
Control Identification Diagnosis