Ph. D. Project
Title:
Synchronization of multi-agent systems with state-dependent topologies and two time-scales dynamics
Dates:
2019/07/16 - 2022/06/13
Other supervisor(s):
DR CNRS Panteley Elena (Elena.PANTELEY@lss.supelec.fr)
Description:
I. State of the art and novelty
Cooperative control of mechanical systems and in particular formation control has recently seen a proliferation of research and applications, primarily due to low cost, robustness and specific application requirements. Industry, market, society, all tend more and more to interconnected systems. Many current engineering problems require multiple systems with local sensing and actions, which have to collaborate in order to accomplish a global goal. The emergence of consensus and synchronization in networks of systems with couplings given by various types of topologies has received much attention [1, 2, 3]. Full or partial synchronization naturally arise in many physical systems such as the brain, flocks of birds, schools of fishes, etc and has to be enforced in some engineering applications, such as for example, fleets of drones or parallel computation implementation. Consequently, control design based on local information and understanding the factors that provide synchronization are important but also challenging problems.

II. Research Plan

In formation control of autonomous vehicles [5,6] it is quite natural to be confronted to scenarios in which the interconnections among the agents are not perennial. In some cases some connections are completely lost and new ones appear; in this case, we say that the network has a time-varying topology. On the other hand, one must also consider the case in which, for a fixed topology, communication channels are shared and, therefore, each pair of communicating agents is allotted specific (of possibly variable duration) intervals of time to use the channel. When both phenomena occur simultaneously, we are confronted to a scenario of time-varying interconnections on two different time scales (see for instance [4]). On the other hand, the design of state-dependent interconnections with special properties to ensure objective achievement for the cooperative system - the theoretical tools developed to analyze heterogeneous systems with time-varying and, even, dynamic interconnections, will be put in use to design consensus-formation control laws for network-interconnected heterogeneous autonomous vehicles. In particular, to address the formation control problem under state-dependent changing topologies, such as in event-triggered control, we will pursue the design of state-dependent and dynamic interconnections with persistency of excitation, in the sense defined in [7].

References
[1] Y. Kuramoto. Chemical Oscillations, Waves and Turbulence. Springer, New York, 1984.
[2] S.H. Strogatz. Sync: The Emerging Science of Spontaneous Order. Hyperion Press, 2003.
[3] D. Gfeller and P. De Los Rios. Spectral coarse graining and synchronization in oscillator networks. Phys. Rev. Lett., 100:174104, 2008.
[4] J. Ben Rejeb, I.-C. Morarescu, J. Daafouz - Control design with guaranteed cost for synchronization in networks of linear singularly perturbed systems. Automatica, Vol 91, 89-97, 2018.
[5] T. Borzone, I.-C. Morãrescu, M. Jungers, M. Boc, C. Janneteau - Hybrid framework for consensus in directed and asynchronous network of non-holonomic agents. IEEE Control Systems Letters (L-CSS), 2(4), 707-712, 2018.
[6] M. Maghenem, A. Loria, and E. Panteley. Formation-tracking control of autonomous vehicles under relaxed persistency of excitation conditions. IEEE Trans. on Control Systems Technology, 2017. Prepublished online. DOI 10.1109/TCST.2017.2734053.
[7] A. Loria, E. Panteley, D. Popovic, and A. Teel. A nested Matrosov theorem and persistency of excitation for uniform convergence in stable non-autonomous systems. IEEE Trans. on Automat. Contr., 50(2):183{198, 2005.
Keywords:
Consensus, multi-agent systems, two-time scales
Department(s): 
Control Identification Diagnosis