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Quadratic stabilization of linear networked control systems via simultaneous protocol and controller design. (English) Zbl 1123.93076

Summary: We derive conditions for quadratic stabilizability of linear networked control systems by dynamic output feedback and communication protocols. These conditions are used to develop a simultaneous design of controllers and protocols in terms of matrix inequalities. The obtained protocols do not require knowledge of controller and plant states but only of the discrepancies between current and the most recently transmitted values of nodes’ signals, and are implementable on controller area networks. We demonstrate on a batch reactor example that our design guarantees quadratic stability with a significantly smaller network throughput than previously available designs.

MSC:

93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
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[1] Artstein, Z., Stabilization with relaxed controls, Nonlinear Analysis, 7, 1163-1173 (1983) · Zbl 0525.93053
[2] Ben Gaid, M. M., & Çela, A. (2005). Model predictive control of systems with communication constraints. In Proceedings of the 16th IFAC world congress; Ben Gaid, M. M., & Çela, A. (2005). Model predictive control of systems with communication constraints. In Proceedings of the 16th IFAC world congress
[3] Beran, E., Vanderberghe, L., & Boyd, S. (1997). A global BMI algorithm based on the generalized benders decomposition. In Proceedings of European control conference; Beran, E., Vanderberghe, L., & Boyd, S. (1997). A global BMI algorithm based on the generalized benders decomposition. In Proceedings of European control conference
[4] Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Studies in applied mathematics; Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Studies in applied mathematics · Zbl 0816.93004
[5] Branicky, M. S., Phillips, S. M., & Zhang, W. (2002). Scheduling and feedback co-design for networked control systems. In Proceedings of the 41st conference on decision and control; Branicky, M. S., Phillips, S. M., & Zhang, W. (2002). Scheduling and feedback co-design for networked control systems. In Proceedings of the 41st conference on decision and control
[6] Goebel, R., Hespanha, J. P., Teel, A. R., Cai, C., & Sanfelice, R. (2004). Hybrid systems: Generalized solutions and robust stability. In Proceedings of the 6th NOLCOS; Goebel, R., Hespanha, J. P., Teel, A. R., Cai, C., & Sanfelice, R. (2004). Hybrid systems: Generalized solutions and robust stability. In Proceedings of the 6th NOLCOS
[7] Goh, K. C., Safonov, M. G., & Papavassilopoulos, G. P. (1994). A global optimization approach for the BMI problem. In Proceedings of 33rd conference on decision and control; Goh, K. C., Safonov, M. G., & Papavassilopoulos, G. P. (1994). A global optimization approach for the BMI problem. In Proceedings of 33rd conference on decision and control
[8] Hassibi, A., How, J., & Boyd, S. (1999). A path-following method for solving BMI problems in control. In Proceedings of the American control conference, USA; Hassibi, A., How, J., & Boyd, S. (1999). A path-following method for solving BMI problems in control. In Proceedings of the American control conference, USA
[9] Hespanha, J. P., Naghshtabrizi, P., & Xu, Y. (2007). A survey of recent results in Networked Control Systems. In Proc. of IEEE special issue on Technology of Networked Control Systems; Hespanha, J. P., Naghshtabrizi, P., & Xu, Y. (2007). A survey of recent results in Networked Control Systems. In Proc. of IEEE special issue on Technology of Networked Control Systems
[10] Hristu-Varsakelis, D. (2001). Feedback control systems as users of a shared network: Communication sequences that guarantee stability. In Proceedings of the 40th conference on decision and control; Hristu-Varsakelis, D. (2001). Feedback control systems as users of a shared network: Communication sequences that guarantee stability. In Proceedings of the 40th conference on decision and control · Zbl 1098.70543
[11] Laila, D. S.; Nesic, D., Changing supply rates for input-output to state stable discrete-time nonlinear systems with applications, Automatica, 39, 821-835 (2001) · Zbl 1032.93073
[12] Lall, S.; Dullerud, G., An LMI solution to the robust synthesis problem for multi-rate sampled-data systems, Automatica, 37, 1909-1922 (2001) · Zbl 1031.93121
[13] Nair, G. N., Fagnani, F., Zampieri, S., & Evans, R. J. (2007). Feedback control under data rate constraints: An overview. In Proc. of IEEE special issue on Technology of Networked Control Systems; Nair, G. N., Fagnani, F., Zampieri, S., & Evans, R. J. (2007). Feedback control under data rate constraints: An overview. In Proc. of IEEE special issue on Technology of Networked Control Systems
[14] Nešić, D.; Teel, A. R., Input-output stability properties of networked control systems, IEEE Transactions on Automatic Control, 49, 1650-1667 (2004) · Zbl 1365.93466
[15] Nešić, D.; Teel, A. R., Input to state stability of networked control systems, Automatica, 40, 2121-2128 (2004) · Zbl 1077.93049
[16] Nešić, D.; Teel, A. R.; Sontag, E. D., Formulas relating KL-stability estimates of discrete-time and sampled-data nonlinear systems, Systems and Control Letters, 38, 49-60 (1999) · Zbl 0948.93057
[17] Palopoli, L., Bicchi, A., & Vincentelli, A. S. (2002). Numerically efficient control of systems with communication constraints. In Proceedings of the 41st conference on decision and control; Palopoli, L., Bicchi, A., & Vincentelli, A. S. (2002). Numerically efficient control of systems with communication constraints. In Proceedings of the 41st conference on decision and control
[18] Prieur, C., & Praly, L. (2004). A tentative direct design of output feedbacks. In Proceedings of 6th NOLCOS; Prieur, C., & Praly, L. (2004). A tentative direct design of output feedbacks. In Proceedings of 6th NOLCOS
[19] Rehbinder, H.; Sanfridson, M., Scheduling of a limited communication channel for optimal control, Automatica, 40, 491-500 (2004) · Zbl 1044.93040
[20] Sontag, E. D., A ‘universal’ construction of Artstein’s theorem on nonlinear stabilization, Systems and Control Letters, 13, 117-123 (1989) · Zbl 0684.93063
[21] Sontag, E. D.; Wang, Y., Output-to-state stability and detectability of nonlinear systems, Systems and Control Letters, 29, 279-290 (1997) · Zbl 0901.93062
[22] Tabbara, M., Nešić, D., & Teel, A. R. (2005). Input-output stability of wireless networked control systems. In Proceedings of the joint 44th conference on decision and control and European control conference; Tabbara, M., Nešić, D., & Teel, A. R. (2005). Input-output stability of wireless networked control systems. In Proceedings of the joint 44th conference on decision and control and European control conference
[23] Walsh, G. C.; Belidman, O.; Bushnell, L. G., Stability analysis of networked control systems, IEEE Transactions on Control Systems Technology, 10, 438-446 (2002)
[24] Walsh, G. C.; Belidman, O.; Bushnell, L. G., Error encoding algorithms for networked control systems, Automatica, 38, 261-267 (2002) · Zbl 0991.93086
[25] Walsh, G. C.; Ye, H., Scheduling of networked control systems, IEEE Control System Magazine, 21, 57-65 (2001)
[26] Walsh, G. C.; Ye, H.; Busnell, L. G., Asymptotic behavior of nonlinear networked control systems, IEEE Transactions on Automatic Control, 46, 1093-1097 (2001) · Zbl 1006.93040
[27] Yook, J. K.; Tilbury, D. M.; Soparkar, N. R., Trading computation for bandwidth: Reducing communication in distributed control systems using state estimators, IEEE Transactions on Control Systems Technology, 10, 503-518 (2002)
[28] Zhang, L., & Hristu-Varsakelis, D. (2005). Stabilization of networked control systems under feedback based communication. In Proceedings of American control conference; Zhang, L., & Hristu-Varsakelis, D. (2005). Stabilization of networked control systems under feedback based communication. In Proceedings of American control conference · Zbl 1117.93302
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