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PhD thesis: Synthesis of robust controllers using symbolic models

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General information

Reference : UMR8506-ANTGIR-004
Workplace : GIF SUR YVETTE
Date of publication : Monday, April 27, 2020
Scientific Responsible name : Antoine Girard
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 1 September 2020
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly

Description of the thesis topic

Scientific context:

Autonomous vehicles, intelligent buildings or robots promise to transform the everyday life of our society in all its dimensions (transport, housing, industry, health, assistance to the elderly...). These systems are examples of cyber-physical systems (CPS) resulting from the integration of computer components and physical processes. The main objective of the PROCSYS project is to provide a framework for CPS programming that enables fast and safe development of their functionality through a high-level programming language. Synthesis algorithms will automatically generate low-level controllers that perform the specified behavior. Correctness of the controllers will be guaranteed by following the correct by construction synthesis paradigm through the use of symbolic control techniques: the continuous physical dynamics is abstracted by a symbolic model, which is a purely discrete dynamical system; an interface consisting of low-level controllers is designed such that the physical system and the symbolic model behaves identically; a high-level symbolic controller is then synthesized automatically from the high-level program and the symbolic model.

Objectives and work description:

The main objective of the thesis is to develop algorithms for the synthesis of robust symbolic controllers. We will build upon our preliminary work on quantitative synthesis of symbolic controllers [4,5]. Using an optimal control formulation, one can synthesize a controller maximizing some robustness margin for safety and reachability specifications. However, this approach does not necessarily guarantee robustness with respect to unmodelled disturbances. In that case, robustness can be achieved through the satisfaction of two main conditions formulated in [3]. Firstly, in the presence of disturbances, the robustness must degrade smoothly with respect to the amplitude of the disturbance. This condition is typically satisfied if the robustness function satisfies some Lipschitz condition. Secondly, in the absence of disturbance, the correct behavior of the system should be restored. This condition will be satisfied if the robustness function satisfies some growth condition with respect to transitions of the symbolic model. To synthesize controllers, which are robust with respect to disturbances, it is thus necessary to include the two types of constraints (Lipschitz and growth conditions) in the optimal control problem to be solved. It will then be necessary to develop algorithms for solving such constrained optimal control problems. The doctoral work will start with simple safety and reachability properties and then extend the approach to more complex specifications defined in the high-level language developed within the PROCSYS project. An evaluation of the proposed algorithms will be done using numerical case studies, e.g. in the field of autonomous driving.

Background of the candidate:

The candidate must hold a Master in control theory or computer science with a strong mathematical background. A prior experience in the area of hybrid systems is recommended. Programming skills are also needed.


[1] Belta, C., Yordanov, B., & Gol, E. A. (2017). Formal Methods for Discrete-Time Dynamical Systems (Vol. 89). Springer.
[2] Tabuada, P. (2009). Verification and control of hybrid systems: a symbolic approach. Springer Science & Business Media.
[3] Rungger, M., & Tabuada, P. (2016). A notion of robustness for cyber-physical systems. IEEE Transactions on Automatic Control, 61(8), 2108-2123.
[4] Eqtami A. and Girard A., Safety control, a quantitative approach. IFAC Conference on Analysis and Design of Hybrid Systems, 2018.
[5] Eqtami A. and Girard A., A quantitative framework for transition systems under reachability specifications. Preprint, 2019.

Work Context

The L2S - Laboratory of Signals and Systems (UMR8506) is a joint research unit CNRS, CentraleSupélec and University Paris Sud, located in Gif-sur-Yvette. The L2S has about 260 people including 108 permanent members, 118 doctoral students and 33 postdocs. It is organized into 3 research divisions (Signal and Statistics Center, Automation and Systems Division and Telecom and Networks Pole). The 3 scientific centers rely on 3 research support divisions: a Human Resources and Communication Management division, a Financial Management division, placed under the responsibility of the director and an IT division. The structure of the unit is completed by a Scientific Computing pole. The budget executed by the laboratory is approximately € 3 million per year.

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