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PhD proposal:  Real-time robust control under varying sampling

Advisors : Daniel Simon and Olivier Sename, INRIA Rhône-Alpes and GIPSA_lab, Grenoble, France

daniel.simon@inria.fr ; olivier.sename@gipsa-lab.grenoble-inp.fr

Framework and objectives :
The proposal fits with the general framework of integrated design between control and realtime
computing. It considers control systems where the control actions are implemented as
multi-tasking real-time systems, under control of distributed computation and communication
resources. Traditional design are based on worst-case consideration, inducing an overdimensioning
of the execution resources. This is no longer acceptable for embedded systems
where the on-board resources are tightly constrained in term, e.g., of computing capabilities
and energy storage.
An appealing alternative consists in the on-line adaptation and regulation of the scheduling
parameters of the real-time control system, in view of the optimisation of the quality of service
provided by the controllers [1-2-5]. However this solution also requires the adaptation of the
process control laws parameters to fit with the computing resources availability, e.g. through
variations of the sampling rates. In particular recent works [1-3-4] have used robust control
theory through Hinf control for Linear Parameter Varying systems, considering the sampling
rate as a varying parameter. On the other hand other works have considered the robustness
of feedback control systems w.r.t. timing disturbances induced by the limited capabilities of the
execution resources, such as jitter and uncontrolled delays [6].

The proposal deals with the development of a codesign methodology for real-time control systems within the framework of LPV systems. The applications to be considered are aerial or underwater drones, for which there already exists high fidelity models and real-time simulators.

The following topics are expected to be handled during the research:

  •  Development of feedback scheduling algorithms based on the control performance

achieved by the plant, to carry out an effective coordination between the controlled
plant and the execution resources (following the preliminary results of [1-2]) ;

  •  Discretization of LPV systems, and synthesis of sampling varying controllers for LPV

systems (follow-up of [4,7]);

  •  Evaluation of LPV based varying sampling controllers w.r.t. execution platform induced

timing disturbances (link between [3-4] and [6]);

  •  Implementation (simulation and experiments) using aerial or underwater drones.

[1] David Robert. Contribution à l’interaction commande/ordonnancement. PhD thesis, I.N.P.
Grenoble/GIPSA-lab , janvier 2007.
[2] Sename, O.; Simon, D.; Ben Gaid, M.; , "A LPV approach to control and real-time
scheduling codesign: Application to a robot-arm control," Decision and Control, 2008. CDC
2008. 47th IEEE Conference on , vol., no., pp.4891-4897, 9-11 Dec. 2008.
[3] Robert, D.; Sename, O.; Simon, D.; , "An Hinf-LPV Design for Sampling Varying
Controllers: Experimentation With a T-Inverted Pendulum," Control Systems Technology,
IEEE Transactions on , vol.18, no.3, pp.741-749, May 2010.
[4] E. Roche : Commande Linéaire à Paramètres Variants discrète à échantillonnage
variable : application à un sous-marin autonome. PhD thesis, Université de Grenoble / GIPSAlab,
octobre 2011.
[5] A. Cervin, J. Eker, B. Bernhardsson, and K.-E. Arzen. Feedback-feedforward scheduling of
control tasks. Real-Time Systems, 23(1), 2002.
[6] Patrick Jocelyn Andrianiaina, Alexandre Seuret, Daniel Simon “Robust control under
weakened real-time constraints” 50th IEEE Conference on Decision and Control, Dec 2011,
Orlando, Floride, U.S.
[7] Tóth, R.: Identification and Modeling of Linear Parameter-Varying Systems. Lecture Notes in
Control and Information Sciences, Vol. 403, Springer, Heidelberg, 2010.

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