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Ph. D. Project : Control and observation of nonlinear systems under limited processing power
Dates : 2017/11/16 - 2020/09/30
Student: Mohamed ID SAID
Manager(s) CRAN: Gilles MILLERIOUX
Full reference: Context

The drop in manufacturing and production costs and the growing computing powers of on-board equipments (micro-controllers for example) have led a huge developments of embedded control in many industrial applications (automotive, aerospace, communication, …). The performances of such equipments are so outstanding that the implementation of advanced control such as optimal control, adaptive control (including the on-line identification of the models) can be reasonably expected. However, if it is sought a use of equipments with low capabilities (in terms of processing time, amount of ressources, size of the memory), and so cheap ones, that would naturally lead to drastically reduce the production cost. Therefore, the search of efficient control methods together with the consideration of limited processing power is very challenging and appears as a timely industrial concern.

Problem statement

First, to be relevant, the dynamic models, even local ones, should often be nonlinear. For those systems, advanced control algorithms are usually very demanding in terms of processing power and are not well suited, or even more is true, are not compatible, with embedded control. This is typically the case when considering optimal control, usually tackled with the help of Pontryagin’s Maximum Principle. In the simplest cases, and so clearly for more intricate problems (low regular dynamics, switched cost functions [1][2]), this approach must be disregarded and alternatives to cope with limited processing power, should be investigated.

An approach would consist in, first, designing a controller regardless from the processing constraints, and then, optimizing the code when performing the implementation. This approach can lead towards a deadlock when drastic constraints must be faced. An alternative, which is the aim of the work, is to take into consideration the processing power since the beginning, that is when designing the control algorithm. It turns out that this issue has not been deeply considered so far, or in any case, in a much lesser extent than other issues related to digital control such as the effect of discretization [3], quantization [4] or communications constraints [5].

Scientific issues and expected work

Distinct solutions will be investigated. The list below is not exclusive.
In the case of optimal control, deriving exact solutions is most often incompatible with limited computation power. Thus, the computation of approximate solutions (in real-time) and the assessment of the impact on the performances will be necessary. A second approach would consist in imposing very simple controller structures (such as on/off controllers). However, from those perspectives, the guarantee of the performances needs to be proved but is a hard task due to a resulting switched structure [6]. Finally, further to the dynamics of the system and the controller, taking into consideration the dynamics induced by the numerical solver, used on-line, would be a convenient way of anticipating the implementation constraints. First investigations have been provided in the case of Model Predictive Control [7].




Working environment
The work will be carried out in Nancy, France. A close cooperation with the Institut Elie Cartan of Lorraine (IECL, Nancy, France) and the University of Sevilla (Spain) is planned. Industrial applications, mostly in the automotive area, will be considered, in particular with the Bosch Research Center in Stuttgart (Germany).

[1] B. Piccoli. Necessary conditions for hybrid optimization. In Decision and Control, 1999. Proceedings of the 38th IEEE Conference on, volume 1, pages 410–415 vol.1, 1999.

[2] H.J. Sussmann. A maximum principle for hybrid optimal control problems. In Decision and Control, 1999. Proceedings of the 38th IEEE Conference on, volume 1, pages 425–430, vol.1, 1999.

[3] EW Djaja, Technique for Enhancing the Performance of Discretized Controllers, IEEE Control Systems, 1999

[4] Y. Sharon and Daniel Liberzon, Input to State Stabilizing Controller for Systems With Coarse Quantization, IEEE Transactions on Automatic Control, vol. 57, no. 4, April 2012

[5] R. Postoyan, P. Tabuada, D. Nesic, and A. Anta, A Framework for the Event-Triggered Stabilization of Nonlinear Systems, IEEE Transactions on Automatic Control, 60(4), 2015.

[6] T. Chambrion and Gilles Millerioux, Hybrid control for low-regular nonlinear systems: application to an embedded control for an electric vehicle (submitted to Autimatica)

[7] T. Manrique-Espindola, M. Fiacchini, T. Chambrion and G. Millerioux, 2016, MPC-based tracking for real-time systems subject to time-varying polytopic constraints, Optimal Control: Applications and Methods, Vol. 37, N. 4, pp. 708-729
Keywords: control and observation, nonlinear systems, embedded systems, optimization
Department(s):
Automatic Control-Identification Diagnosis