PhD thesis proposal: Contract-based approaches for control and monitoring of cyber-physical systems: application to the electrical transmission grid
Supervisors: Antoine Girard (Antoine.Girard@l2s.centralesupelec.fr)
Alessio Iovine (Alessio.Iovine@l2s.centralesupelec.fr)
Location: Laboratoire des Signaux et Systèmes - L2S
CentraleSupélec – CNRS – Univ. Paris-Saclay
Gif-sur-Yvette, France
Dates: 3 years, starting at latest fall 2023
Salary: 2300 euro monthly, gross salary
Context:
Cyber-physical systems (CPSs) [1] consist of physical systems augmented with computation and communication infrastructure making it possible to design highly dynamic systems able to perform efficiently under high uncertainty. CPSs are often deployed at large scale, which makes the design of such system a real challenge in modern engineering. An example of large-scale CPS is the modern electrical transmission grid which includes new types of components such as renewable energy generators (e.g. wind farms) or energy storage devices (e.g. batteries) that offer great opportunities for low-carbon energy production but at the same time poses great challenges from the grid stability viewpoint.
Contract theory [2,3] is a promising framework for rigorous component-based design of highly dynamic distributed systems. Intuitively, a contract is a formal specification consisting of pairs of assumptions and guarantees. A guarantee describes the task that the component must fulfill when its environment (made of other components and of the external environment) satisfies the associated assumption. Hence, assume-guarantee contracts make it possible to design components that can adapt under various working conditions. Moreover, compositional reasoning makes it possible to prove properties of the global systems based on the contracts satisfied by its components.
Several recent works have explored contract theory from a control perspective [4-9]. In [10], we introduced a general class of assume-guarantee contract and characterized contract satisfaction in term of invariant sets for an extended dynamical system.
Research program:
In this doctoral work, we will build on the preliminary results of [10] to design new methodologies for contract-based design of CPSs. We aim at tackling the following problems:
• Verification: given a contract and a component model, verify that the contract is satisfied. We will develop tools based on invariant sets which will allow us to leverage existing techniques such as set theoretic methods [11], abstraction-based [12] and data-driven approaches [13].
• Controller synthesis: given a contract and a component model, synthesize a controller that fulfills the contract. We are particularly interested in designing model predictive control approaches that provably enforce assume-guarantee contracts even beyond their prediction horizon.
• Monitoring algorithms: given a contract and a component model, design a monitor that raises an alarm when a contract is violated. We aim at designing predictive algorithms able to raise alarms even before the contract is violated.
The proposed methodologies will be evaluated on use cases from the electrical transmission grid. The PhD thesis will be attached to the activities of the RTE chair.
References:
[1] P. Derler, E. A. Lee, and A. Sangiovanni Vincentelli, “Modeling cyber–physical systems,” Proceedings of the IEEE, vol. 100, no. 1, pp. 13–28, 2012.
[2] A. Benveniste, B. Caillaud, D. Nickovic, R. Passerone, J.-B. Raclet, P. Reinkemeier, A. Sangiovanni-Vincentelli, W. Damm, T. Henzinger, and K. Larsen, “Contracts for system design,” Foundations and Trends in Electronic Design Automation, vol. 12, no. 2-3, pp. 124–400, 2018.
[3] A. Sangiovanni-Vincentelli, W. Damm, and R. Passerone, “Taming dr. frankenstein: Contract-based design for cyber-physical systems,” European Journal of Control, vol. 18, no. 3, pp. 217–238, 2012.
[4] B. Besselink, K. H. Johansson, and A. Van Der Schaft, “Contracts as specifications for dynamical systems in driving variable form,” in European Control Conference, 2019.
[5] A. Saoud, A. Girard, and L. Fribourg, “Assume-guarantee contracts for continuous-time systems,” Automatica, vol. 134, p. 109910, 2021.
[6] M. Sharf, B. Besselink, A. Molin, Q. Zhao, and K. H. Johansson, “Assume/guarantee contracts for dynamical systems: Theory and computational tools,” IFAC-PapersOnLine, vol. 54, no. 5, pp. 25–30, 2021.
[7] Y. Chen, J. Anderson, K. Kalsi, S. H. Low, and A. D. Ames, “Compositional set invariance in network systems with assume-guarantee contracts,” in 2019 American Control Conference (ACC), pp. 1027–1034, 2019.
[8] B. Shali, A. van der Schaft, and B. Besselink, “Behavioural contracts for linear dynamical systems: input assumptions and output guarantees,” in 2021 European Control Conference (ECC), pp. 567–572, IEEE, 2021.
[9] A. Saoud, A. Girard, and L. Fribourg, “Contract-based design of symbolic controllers for safety in distributed multiperiodic sampled data systems,” IEEE Transactions on Automatic Control, vol. 66, no. 3, pp. 1055–1070, 2020.
[10] A. Girard, A. Iovine, and S. Benberkane, “Invariant Sets for Assume-Guarantee Contracts”, IEEE Conference on Decision and Control, 2022.
[11] F. Blanchini and S. Miani, Set-Theoretic Methods in Control. Systems & Control: Foundations & Applications, Birkhauser Boston, 2007.
[12] P. Tabuada, Verification and control of hybrid systems: a symbolic approach. Springer Science & Business Media. 2009.
[13] Z. Wang and R. M. Jungers, “A data-driven method for computing polyhedral invariant sets of black-box switched linear systems,” IEEE Control Systems Letters, vol. 5, no. 5, pp. 1843–1848, 2021
