On distributed symbolic control of interconnected systems under persistency specifications

• Autorzy: Apaza-Perez W. Alejandro , Combastel Christophe , Zolghadri Ali

Identyfikatory

DOI

10.34768/amcs-2020-0046

• Języki publikacji: EN

Abstrakty

EN

This paper presents an abstraction-based technique to solve the problem of distributed controller design enforcing persistency specifications for interconnected systems. For each subsystem, controller synthesis is based on local distributed sensor information from other subsystems. An effective method is presented for quantification of such partial information in an abstraction in terms of level sets of Lyapunov-like ranking functions. The results are illustrated on a laboratory hydraulic system.

Słowa kluczowe

EN

symbolic controller synthesis; distributed controller; interconnected system

PL

synteza kontrolera; rozproszony system sterowania; system połączony

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 4
• Strony: 629--639
• Opis fizyczny: Bibliogr. 45 poz., rys., tab.

Twórcy

autor

Apaza-Perez W. Alejandro

• IMS Laboratory, University of Bordeaux—CNRS, 351 Cours de la Libération, 33405 Talence, France

autor

Combastel Christophe

• IMS Laboratory, University of Bordeaux—CNRS, 351 Cours de la Libération, 33405 Talence, France

autor

Zolghadri Ali

• IMS Laboratory, University of Bordeaux—CNRS, 351 Cours de la Libération, 33405 Talence, France

Bibliografia

• [1] Apaza-Perez, W.A., Combastel, C. and Zolghadri, A. (2019). Abstraction-based low complexity controller synthesis for interconnected non-deterministic systems, 18th European Control Conference (ECC), Naples, Italy, pp. 4174–4179.
• [2] Belta, C., Yordanov, B. and Göl, E. (2017). Formal Methods for Discrete-Time Dynamical Systems, Springer, Cham.
• [3] Borri, A., Pola, G. and Benedetto, M.D.D. (2012). A symbolic approach to the design of nonlinear networked control systems, 15th ACM International Conference on Hybrid Systems: Computation and Control, HSCC’12, Beijing, China, pp. 255–264.
• [4] Borri, A., Pola, G. and Benedetto, M.D.D. (2019). Design of symbolic controllers for networked control systems, IEEE Transactions on Automatic Control 64(3): 1034–1046.
• [5] Chen, Y., Anderson, J., Kalsi, K., Low, S.H. and Ames, A.D. (2019). Compositional set invariance in network systems with assume-guarantee contracts, 2019 American Control Conference (ACC), Philadelphia, PA, USA, pp. 1027–1034.
• [6]Coënt, A.L., Fribourg, L., Markey, N., Vuyst, F.D. and Chamoin, L. (2016). Distributed synthesis of state-dependent switching control, in K.G. Larsen et al. (Eds), Reachability Problems, Springer, Cham, pp. 119–133.
• [7] Dallal, E. and Tabuada, P. (2015). On compositional symbolic controller synthesis inspired by small-gain theorems, 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, pp. 6133–6138.
• [8] Dashkovskiy, S.N., Rüffer, B.S. and Wirth, F.R. (2010). Small gain theorems for large scale systems and construction of ISS Lyapunov functions, SIAM Journal on Control and Optimization 48(6): 4089–4118.
• [9] Eqtami, A. and Girard, A. (2019). A quantitative approach on assume-guarantee contracts for safety of interconnected systems, 18th European Control Conference (ECC), Naples, Italy, pp. 536–541.
• [10] Ge, X., Yang, F. and Han, Q.L. (2017). Distributed networked control systems: A brief overview, Information Sciences 380: 117–131.
• [11] Ghasemi, K., Sadraddini, S. and Belta, C. (2020). Compositional synthesis via a convex parameterization of assume-guarantee contracts, 23rd International Conference on Hybrid Systems: Computation and Control, HSCC’20, Sydney, Australia.
• [12] Girard, A., Gössler, G. and Mouelhi, S. (2016). Safety controller synthesis for incrementally stable switched systems using multiscale symbolic models, IEEE Transactions on Automatic Control 61(6): 1537–1549.
• [13] Girard, A. and Pappas, G.J. (2011). Approximate bisimulation: A bridge between computer science and control theory, European Journal of Control 17(5): 568–578.
• [14] Gruber, F., Kim, E.S. and Arcak, M. (2017). Sparsity-aware finite abstraction, 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, Australia, pp. 2366–2371.
• [15] Henzinger, T.A., Qadeer, S., Rajamani, S.K. and Tasiran, S. (2002). An assume-guarantee rule for checking simulation, ACM Transactions on Programming Languages and Systems 24(1): 51–64.
• [16] Jabri, D., Guelton, K., Belkhiat, D.E.C. and Manamanni, N. (2020). Decentralized static output tracking control of interconnected and disturbed Takagi–Sugeno systems, International Journal of Applied Mathematics and Computer Science 30(2): 225–238, DOI: 10.34768/amcs-2020-0018.
• [17] Jiang, Z.P., Teel, A.R. and Praly, L. (1994). Small-gain theorem for ISS systems and applications, Mathematics of Control, Signals and Systems 7(2): 95–120.
• [18] Kamiński, M. (2015). Symbolic computing in probabilistic and stochastic analysis, International Journal of Applied Mathematics and Computer Science 25(4): 961–973, DOI: 10.1515/amcs-2015-0069.
• [19] Kim, E.S., Arcak, M. and Seshia, S.A. (2015). Compositional controller synthesis for vehicular traffic networks, 2015 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, pp. 6165–6171.
• [20] Majumdar, R. and Zamani, M. (2012). Approximately bisimilar symbolic models for digital control systems, in P. Madhusudan and S.A. Seshia (Eds), Computer Aided Verification, Springer, Berlin/Heidelberg, pp. 362–377.
• [21] Mazo, M., Davitian, A. and Tabuada, P. (2010). PESSOA: A tool for embedded controller synthesis, in T. Touili et al. (Eds), Computer Aided Verification, Springer, Berlin/Heidelberg, pp. 566–569.
• [22] Meyer, P. and Dimarogonas, D.V. (2017). Compositional abstraction refinement for control synthesis under lasso-shaped specifications, 2017 American Control Conference (ACC), Seattle, WA, USA, pp. 523–528.
• [23] Meyer, P., Girard, A. and Witrant, E. (2018). Compositional abstraction and safety synthesis using overlapping symbolic models, IEEE Transactions on Automatic Control 63(6): 1835–1841.
• [24] Mouelhi, S., Girard, A. and Gossler, G. (2013). COSYMA: A tool for controller synthesis using multi-scale abstractions, 16th International Conference on Hybrid Systems: Computation and Control, HSCC’13, Philadelphia, PA, USA, pp. 83–88.
• [25] Nilsson, L.P. (2017). Correct-by-Construction Control Synthesis for High-Dimensional Systems, PhD thesis, University of Michigan, Ann Arbor, MI.
• [26] Nilsson, P. and Ozay, N. (2020). Control synthesis for permutation-symmetric high-dimensional systems with counting constraints, IEEE Transactions on Automatic Control 65(2): 461–476.
• [27] Pola, G., Girard, A. and Tabuada, P. (2008). Approximately bisimilar symbolic models for nonlinear control systems, Automatica 44(10): 2508–2516.
• [28] Pola, G., Pepe, P. and Benedetto, M.D.D. (2018). Decentralized supervisory control of networks of nonlinear control systems, IEEE Transactions on Automatic Control 63(9): 2803–2817.
• [29] Pola, G., Pepe, P., Benedetto, M.D.D. and Tabuada, P. (2010). Symbolic models for nonlinear time-delay systems using approximate bisimulations, Systems & Control Letters 59(6): 365–373.
• [30] Reissig, G. (2011). Computing abstractions of nonlinear systems, IEEE Transactions on Automatic Control 56(11): 2583–2598.
• [31] Reissig, G., Weber, A. and Rungger, M. (2017). Feedback refinement relations for the synthesis of symbolic controllers, IEEE Transactions on Automatic Control 62(4): 1781–1796.
• [32] Rungger, M. and Zamani, M. (2016). Scots: A tool for the synthesis of symbolic controllers, 19th International Conference on Hybrid Systems: Computation and Control, HSCC’16, Vienna, Austria, pp. 99–104.
• [33] Saoud, A. (2019). Compositional and Efficient Controller Synthesis for Cyber-Physical Systems, PhD thesis, Université Paris-Saclay, Gif sur Yvette.
• [34] Saoud, A., Girard, A. and Fribourg, L. (2019). Assume-guarantee contracts for discrete and continuous-time systems, Preprint, https://hal.archives-ouvertes.fr/hal-02196511.
• [35] Saoud, A., Girard, A. and Fribourg, L. (2020). Contract-based design of symbolic controllers for safety in distributed multiperiodic sampled-data systems, IEEE Transactions on Automatic Control, DOI:10.1109/TAC.2020.2992446.
• [36] Saoud, A., Jagtap, P., Zamani, M. and Girard, A. (2018). Compositional abstraction-based synthesis for cascade discrete-time control systems, 6th IFAC Conference on Analysis and Design of Hybrid System, Oxford, UK.
• [37] Tabuada, P. (2009). Verification and Control of Hybrid Systems, Springer, New York, NY.
• [38] Tazaki, Y. and Imura, J. (2012). Discrete abstractions of nonlinear systems based on error propagation analysis, IEEE Transactions on Automatic Control 57(3): 550–564.
• [39] Weber, A., Rungger, M. and Reissig, G. (2017). Optimized state space grids for abstractions, IEEE Transactions on Automatic Control 62(11): 5816–5821.
• [40] Wongpiromsarn, T., Topcu, U., Ozay, N., Xu, H. and Murray, R. (2011). Tulip: A software toolbox for receding horizon temporal logic planning, 14th International Conference on Hybrid Systems: Computation and Control, HSCC’11, Chicago, IL, USA, pp. 313–314.
• [41] Zamani, M., Esfahani, P.M., Majumdar, R., Abate, A. and Lygeros, J. (2014). Symbolic control of stochastic systems via approximately bisimilar finite abstractions, IEEE Transactions on Automatic Control 59(12): 3135–3150.
• [42] Zamani, M., Pola, G., Mazo, M. and Tabuada, P. (2012). Symbolic models for nonlinear control systems without stability assumptions, IEEE Transactions on Automatic Control 57(7): 1804–1809.
• [43] Zhai, G., Chen, N. and Gui, W. (2013). Decentralized design of interconnected H∞ feedback control systems with quantized signals, International Journal of Applied Mathematics and Computer Science 23(2): 317–325, DOI:10.2478/amcs-2013-0024.
• [44] Zolghadri, A., Henry, D. and Monsion, M. (1996). Design of nonlinear observers for fault diagnosis: A case study, Control Engineering Practice 4(11): 1535–1544.
• [45] Zonetti, D., Saoud, A., Girard, A. and Fribourg, L. (2019). A symbolic approach to voltage stability and power sharing in time-varying DC microgrids, 2019 18th European Control Conference (ECC), Naples, Italy, pp. 903–909.