France: PhD student required in Research Center on Automatic Control of Nancy

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Description: We are searching for an exceptional Ph.D. student with a strong background in dynamical systems and automatic control to work at Research Center on Automatic Control of Nancy (CRAN – Centre de Recherche en Automatique de Nancy). This work will be developed in the framework of the “Computation Aware Control Systems” ANR project. Our strategies should not only be able to decide which control actions need to be taken, but also when the control tasks should be scheduled based on the availability of computing units and the state of the physical plant. The overall concept of our project is based on the fact that, in order to design computation aware control systems, a serious effort is needed to develop theoretical techniques in controller synthesis for hybrid systems. Nowadays, the systems are seen as parts of networks. Each vertex of the network is influenced by the others but it has to be controlled with a minimum/local amount of knowledge on their behavior. This viewpoint opened a new research direction situated at the intersection of the graph theory, the information theory and the control theory. The networked systems are modeled as graphs and the control design is realized using spectral properties of the adjacency and Laplacian matrices associated to the graphs. The control of networked linear systems is now well developed and understood.
Recent techniques proposed for computation aware control design lead to dynamical systems with finite state jumps at some discrete instants of time. These systems are known in the literature either as impulsive or reset systems. The existing literature treats mostly linear reset systems. Two types of reset rules may be encountered, those defined by a time condition and those defined by a state one. The former type of reset systems is usually defined by a periodic or quasi-periodic reset rule. The later type assumes the stability of the system inside a given set and limits the evolution of the system to this set. The reset is done when the trajectory gets out of the stability set. The stability analysis as well as the stabilization of the both types is realized via Lyapunov techniques. Precisely, adequate (quasi-) quadratic Lyapunov functions are obtained by solving certain sets of linear matrix inequalities (LMI). The aim of the PhD thesis is to analyze networked reset systems. Our focus will be on systems with a state dependent reset rule. The admissible
evolution set will be described by some unilateral constraints and a complementarity relation will allow us to detect the reset instants. The reset rule at the impact with one or several constraints will be given by  kind of Newton restitution law. Doing so, we will be able to assure that the system evolves only inside the admissible domain. By using the complementarity framework, we expect to get further understanding of the stability and stabilization of reset systems. Since the complementarity formalism is not restricted to linear systems we also expect that using this tool we will be able to extend the analysis to nonlinear systems.

Applications and related questions have to be directed to:
Dr. Irinel-Constantin Morarescu
Prof. Jamal Daafouz

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