Adaptive control of non-linearly parameterized systems and applications

21 Mar 2024
Job Information

Organisation/Company

Université Gustave Eiffel - Site de Versailles

Research Field

Mathematics
Computer science » Cybernetics

Researcher Profile

Recognised Researcher (R2)
Leading Researcher (R4)
First Stage Researcher (R1)
Established Researcher (R3)

Country

France

Application Deadline

2 Apr 2024 - 22:00 (UTC)

Type of Contract

Temporary

Job Status

Full-time

Offer Starting Date

1 Oct 2024

Is the job funded through the EU Research Framework Programme?

Not funded by an EU programme

Is the Job related to staff position within a Research Infrastructure?

No

Offer Description

Adaptive control of non-linearly parameterized systems and applications

 

Context: Adaptive control makes it possible to control a system despite uncertainties in its parameters. It offers solutions in multiple application domains. However, there still exists a certain number of theoretical challenges to solve to allow the control of a certain number of systems, notably in mobility. This work is then in the frame of the COSYS department (of the Gustave Eiffel University) project whose ambition is “to develop the concepts and necessary tools to improve the knowledge, the methods, the technologies and the operational systems towards a renewed intelligence of mobility”. It is in the scientific pillar of COSYS “automation, control, optimization”.

In the literature, it is almost systematically adopted the hypothesis of the linearity in the parameters in the adaptive control synthesis [13]. Very few results exist for the case when the parameters enter non-linearly, whether numerous applications exist with the parameters entering non-linearly in the physical model that describes the system. This is the case for example, in robotics, of the visual servoing problem [15]; in mechanics, of the friction compensation problem; in electronics, of RLC circuit models; in vehicle control, by taking into account the wheel slip when braking the vehicle [7] or by the control of models (that are linear but NL-parameterized) of the lateral mode of the vehicle; in humans mobility, by the control of models of the functional electrical stimulation of the muscles with the goal of rehabilitation [5], or still; in energy, by the photovoltaic panels control [3].

The control synthesis for these systems is done frequently, whenever possible, by a linearization, therefore restraining the validity domain of the control (see for example [6] for vehicle braking systems and [3] for the photovoltaic panels control).

Some few results have appeared in these last decades for the adaptive control of nonlinearly parameterized (NLP) systems notably for the case when the parameterizations are convex or concave [2].

We have proposed an NLP algorithm dedicated to the control of certain classes of nonlinear and nonlinearly parameterized systems with multilinear parameterization [9], [14], [4] et [10] that satisfy certain matching conditions (the control input appears in an additive form to the nonlinearity). We have recently applied these results to the wheel slip regulation during vehicle braking [11]. We have also carried out a comparative study showing that the NLP control is much superior than the control of the approximated linearly parameterized (LP) model [12]. We have also pushed ahead with the study by simulating the LP and the NLP controllers taking into account the Pacejka wheels-road contact forces in the simulated plant. Whether the NLP controller continues to follow the reference even in difficult scenarios like snow, the LP controller is not able anymore to follow the reference and diverges.

 

Objectives: The goal of this thesis is to extend our NLP approach by considering different theoretical objectives. These objectives are structured in three different parts:

1) To study the conditions for parametric convergence of the adaptive NLP controller that we have developed [10]. This involves important challenges because the parameter convergence theories of LP systems do not apply to NLP systems. Some few results on parametric convergence of NLP systems are proposed in the literature like [8] which establishes the parametric convergence conditions for the algorithm proposed in [2].

2) To extend our approach in [10] to other types of systems, in which the matching condition is not satisfied anymore (the control input does not appear anymore in an additive form to the nonlinearity). In this frame, we wish to study systems in a triangular form, like those that contain one or more integrators between the control input and the variable to be controlled. And,
3) To control linear nonlinearly parameterized systems, with the goal of controlling the vehicle Ackerman model without over-parameterizing the system, such to augment the set of solutions in an optimization problem.

Method: Steps of the work. The first step of the thesis work will consist of a bibliographical study on the adaptive control of nonlinearly parameterized systems. The goal of this step is to create a scientific background on the topic for the PhD student. The second step of the work consists in the study of our current algorithm [10]. For this, the thesis director will explain in details the approach to the PhD student. This step is very important and the PhD student will need to understand in deepness what has been done before working to extend the present results. In the third step, the PhD student will effectively work on the thesis topic to address the three goal explained above. For this, for goals (1) and (2), the method will consist in studying the solutions proposed to the algorithm [2] (for the parametric convergence [8] and for the triangular form [1]) to detect possible similarities to the extensions that we wish to carry out to our algorithm in [10]. This will facilitate the theoretical development that we wish to carry out. The goal (3) above will be tackled via simplified models. Once a theoretical result is achieved, and before tackling the next one, the PhD student will carry out simulations to study the theoretical result that has been just achieved. For finalizing the work, a practical problem will then be chosen, to apply and study through simulations, the developed theory.

We collaborate in these topics with the Federal University of Rio de Janeiro (COPPE), in Brazil, and with the MIT, in the USA. It is possible to have interactions with our colleagues in these institutions by distance.

Profile: Solid theoretical basis in mathematics and/or in control are essential. The knowledge of simulation softwares Maltab/Simulik is important.

Laboratory: PICS-L, https://pics-l.univ-gustave-eiffel.fr/ in Versailles Campus – 25, Allée des Marronniers, 78000, Versailles-Satory.

Thesis Advisor: Mariana Netto https://pagespro.univ-gustave-eiffel.fr/mariana-netto , Tenured researcher, PICS-L/COSYS, Université Gustave Eiffel.

Doctoral School : STIC - Sciences et technologies de l'Information et de la Communication, Université Paris Saclay.

Financing: Doctoral Contract at Gustave Eiffel University.

Procedure:

To contact by email the Thesis Director Mariana Netto until 03 avril 2024. It is asked to send in the email the candidate’s grades of his(her) Master’s (or M1 et M2 in France), the CV and a motivation letter .

The thesis director will exchange then with the admissible candidates on the possibility to answer to this call.

To write the thesis project in 4 pages with the thesis director.

The pre-selected candidate will candidate on-line until 12 April midnight.

 

Bibliography:
[1] A. Kojic, A. Annaswamy, A.-P. Loh and R. Lozano. Adaptive control of a class of nonlinear systems with convex/concave parameterization, Systems & Control Letters, vol. 37, no. 5, pp. 267-274, 1999.

[2] A.M. Annaswamy, F.P. Skantze, and A.P. Loh, “Adaptive control of continuous-time systems with convex/concave parametrization”, Automatica, vol. 34, no. 1, pp. 33–49, 1998.
[3] F. Jaramillo-Lopez, G. Damm, G. Kenne and F. Lamnabhi-Lagarrigue. Adaptive control scheme for maximum power point tracking of a photovoltaic system connected to the grid. 2013 European Control Conference (ECC), July 17-19, 2013, Zürich, Switzerland.

[4] M.S. Netto and A. Annaswamy, “Adaptive control of a class of multilinearly parameterized systems by using noncertainty equivalence control”, in Proc. Conference on Decision and Control, Maui, Hawaii, USA, 10-13 December 2012.
[5] R. Ortega, A. Bobtsov, M. de Queiroz, R. Yang, and N. Nikolaev, “A Globally Stable Adaptive Controller for the Human Shank Dynamics,” ASME J. Dyn. Syst., Meas., and Control, doi: https://doi.org/10.1115/1.4062617 , in press.
[6] S. Choi (2008). Antilock brake system with a continuous wheel slip control to maximize the braking performance and the ride quality. IEEE Transactions on Control Systems Technology, 16(5), pp. 996–1003.
[7] T. B. Hoàng, W. Pasillas-Lépine, A. De Bernardinis, and M. Netto. Extended Braking Stiffness Estimation Based on a Switched Observer with an Application to Wheel-Acceleration Control. IEEE Transactions on Control Systems Technology, vol. 22, no. 6, 2014.
[8] C. Cao, A. Annaswamy and A. Kojic. Parameter Convergence in Nonlinearly Parameterized Systems IEEE Transactions on Automatic Control, Vol. 48, No. 3, 2003.
[9] M. Netto, A.M. Annaswamy, R. Ortega, and M. Moya, “Adaptive control of a class of nonlinearly parametrized systems using convexification”, Internat. J. Control, vol. 73, no. 14, pp. 1312–1321, 2000.
[10] M. Netto, A. Annaswamy, R. Costa, A. J. Peixoto and R. Sainct. “Non-certainty adaptive control of NL-parameterized systems: parameterizations depending on the state with varying sign”, To be submitted.
[11] M. Netto, A. Annaswamy, W. Pasillas-Lépine, R. Costa, A.J. Peixoto. “Wheel slip Control: a non-linearly parameterized approach”, Internal report, 2022.
[12] H. Al Fares. ``Commande adaptative non-linéaire et applications: la régulation du taux de glissement des roues d’un véhicule via une étude comparative’’, rapport de stage de M2, Master ATSI, 2023.
[13] A. Annaswamy and A.L. Fradkov. A historical perspective of adaptive control and learning. Annual Reviews in Control, vol. 52, pp. 18–41, 2021.
[14] M. Netto, A.M. Annaswamy, S. Mammar, and N. Minoiu, “A new adaptive controller for systems with multilinear parameterization”, ISTE Book, pp. 505–521, 2006.
[15] L. Hsu, R.R. Costa, and P. Aquino, “Stable adaptive visual servoing for moving targets”, in Proc. of the American Control Conference (ACC), Chicago, June 2000.

Funding category: Contrat doctoral
Le montant du contrat doctoral alloué par l'IFSTTAR est actuellement de 1858 € bruts mensuels pendant les deux premières années et de 2165 € bruts mensuels la troisième année. Le candidat devra candidater et passer par un processus de sélection pour l'atribution du financement.
PHD Country: France

Requirements
Specific Requirements

Solid theoretical basis in control and/or mathematics are essential. The knowledge of simulation softwares Maltab/Simulik is important.

Additional Information
Work Location(s)

Number of offers available

1

Company/Institute

Université Gustave Eiffel - Site de Versailles

Country

France

City

Versailles

Geofield

Where to apply

Website

https://www.abg.asso.fr/fr/candidatOffres/show/id_offre/121506

Contact

Website

https://www.univ-gustave-eiffel.fr/

STATUS: EXPIRED