Abstract
In physical dynamical systems equipped with embedded controllers, timing contracts specify the time instants at which certain operations are performed such as sampling, computation, and actuation. In the first part of this chapter, we present a class of timing contracts specifying bounds on the sampling-to-actuation delay and on the sampling period. We then review existing techniques that can handle the problem of stability verification: given models of the physical plant and of the controller and a timing contract, we verify that the resulting dynamical system is stable. In the second part of the chapter, we consider the scheduling problem of embedded controllers on a multiple core computational platform: given a set of controllers, each of which is subject to a timing contract, we synthesize a dynamic scheduling policy, which guarantees that each timing contract is satisfied and that each of the shared computational resources is allocated to at most one embedded controller at any time. The approach is based on a timed game formulation whose solution provides a suitable schedule.
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References
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Al Khatib, M., Girard, A., Dang. T.: Verification and synthesis of timing contracts for embedded controllers. Hybrid Systems: Computation and Control, pp. 115–124. ACM (2016)
Al Khatib, M., Girard, A., Dang, T., Dang, T.: Stability verification and timing contract synthesis for linear impulsive systems using reachability analysis. Nonlinear Anal. Hybrid Syst, 25, 211–226 (2017)
Al Khatib, M., Girard, A., Dang, T.: Scheduling of embedded controllers under timing contracts. Hybrid Systems: Computation and Control, pp. 131–140. ACM (2017)
Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: UPPAAL-TIGA: time for playing games! Computer Aided Verification, pp. 121–125. Springer (2007)
Bauer, N.W., Maas, P.J.H., Heemels, W.P.M.H.: Stability analysis of networked control systems: a sum of squares approach. Automatica 48(8), 1514–1524 (2012)
Briat, C.: Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints. Automatica 49(11), 3449–3457 (2013)
Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. Concurrency Theory, pp. 66–80. Springer, Berlin (2005)
Cloosterman, M.B.G., Hetel, L., Van De Wouw, N., Heemels, W.P.M.H., Daafouz, J., Nijmeijer, H.: Controller synthesis for networked control systems. Automatica 46(10), 1584–1594 (2010)
Donkers, M.C.F., Heemels, W.P.M.H., Van De Wouw, N., Hetel, L.: Stability analysis of networked control systems using a switched linear systems approach. IEEE Trans. Autom. Control 56(9), 2101–2115 (2011)
Derler, P., Lee, E.A., Tripakis, S., Törngren, M.: Cyber-physical system design contracts. In: International Conference on Cyber-Physical Systems, pages 109–118 (2013)
Fiacchini, M., Morărescu, I.-C.: Constructive necessary and sufficient condition for the stability of quasi-periodic linear impulsive systems. IEEE Trans. Autom. Control 61(9), 2512–2517 (2016)
Fujioka, H.: Stability analysis of systems with aperiodic sample-and-hold devices. Automatica 45(3), 771–775 (2009)
Gao, H., Meng, X., Chen, T., Lam, J.: Stabilization of networked control systems via dynamic output-feedback controllers. SIAM J. Control Optim. 48(5), 3643–3658 (2010)
Hetel, L., Daafouz, J., Tarbouriech, S., Prieur, C.: Stabilization of linear impulsive systems through a nearly-periodic reset. Nonlinear Anal. Hybrid Syst. 7(1), 4–15 (2013)
Hetel, L., Kruszewski, A., Perruquetti, W., Richard, J.-P.: Discrete and intersample analysis of systems with aperiodic sampling. IEEE Trans. Autom. Control 56(7), 1696–1701 (2011)
Heemels, W.P.M.H., Teel, A.R., Van de Wouw, N., Nešić, D.: Networked control systems with communication constraints: tradeoffs between transmission intervals, delays and performance. IEEE Trans. Autom. Control 55(8), 1781–1796 (2010)
Liu, K., Fridman, E., Hetel, L.: Networked control systems in the presence of scheduling protocols and communication delays. SIAM J. Control Optim. 53(4), 1768–1788 (2015)
Le Guernic, C., Girard, A.: Reachability analysis of linear systems using support functions. Nonlinear Anal. Hybrid Syst. 4(2), 250–262 (2010)
Liu, K., Suplin, V., Fridman, E.: Stability of linear systems with general sawtooth delay. IMA J. Math. Control Inf. 27(4), 419–436 (2010)
Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: Annual Symposium on Theoretical Aspects of Computer Science, pp. 229–242. Springer (1995)
Seuret, A., Peet, M.: Stability analysis of sampled-data systems using sum of squares. IEEE Trans. Autom. Control 58(6), 1620–1625 (2013)
Acknowledgements
This work was supported by the Agence Nationale de la Recherche (COMPACS project ANR-13-BS03-0004) and by the Labex DigiCosme, Université Paris-Saclay (CODECSYS project).
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Al Khatib, M., Girard, A., Dang, T. (2018). Timing Contracts for Multi-Core Embedded Control Systems. In: Tarbouriech, S., Girard, A., Hetel, L. (eds) Control Subject to Computational and Communication Constraints. Lecture Notes in Control and Information Sciences, vol 475. Springer, Cham. https://doi.org/10.1007/978-3-319-78449-6_6
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DOI: https://doi.org/10.1007/978-3-319-78449-6_6
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