Control Óptimo- L2 Basado en Red Mediante Funcionales de Lyapunov-Krasovskii
Publicado en 2012;09:14-23. - vol.09 núm 01
Resumen
Resumen
En el presente trabajo se estudia el control óptimo con rechazo de perturbaciones L2 para sistemas lineales controlados a través de red. En estos sistemas el lazo de control se cierra utilizando una red de comunicaciones. Entre los problemas que introduce la red se encuentran posibles retrasos, en general aleatorios, así como pérdidas de paquetes. Desde un enfoque basado en funcionales de Lyapunov- Krasovskii (LKF) se aborda el diseño de controladores óptimos que, dado un nivel deseado de atenuación de perturbaciones, estabilicen el sistema minimizando a su vez un funcional de coste. En el artículo se desarrolla, en primer lugar, una formulación y solución general para el problema. Posteriormente, se resuelve para un funcional de Lyapunov-Krasovskii particular. El comportamiento de los controladores obtenidos se compara con el dado por un control clásico LQR en un escenario de control de distancia en carretera.
Palabras clave Redes de comunicación. Compensación de retrasos. Métodos de Lyapunov. Control óptimo. Retardo temporal.
Introducción
Referencias no citadas
(Azimi-Sadjadi, 2003), (Branicky et al., 1998), (Delfour et al., 1975), (Dormido et al., 2008), (El Ghaoui et al., 1997), (Esfahani et al., 1998), (Gupta et al., 2007), (Hale and Verduyn Lunel, 1993), (Hespanha et al., 2007), (Hokayem and Abdallah, 2004), (Jiang and Han, 2008), (Jiang et al., 2008), (Kharatishvili, 1961), (Kosmidou and Boutalis, 2006), (Krasovskii, 1962), (Mahmoud, 2000), (Meng et al., 2009), (Mikheev et al., 1988), (Naghshtabrizi and Hespanha, 2005), (Nikolakopoulos et al., 2008), (Ross and Flugge-Lotz, 1969), (Salt et al., 2008), (Shao, 2009), (Sinopoli et al., 2005), (Tatikonda and Mitter, 2004), (Xiong and Lam, 2007), (Xu and Lam, 2007), (Xu and Lam, 2008), (Yue et al., 2005), (Zampieri, 2008), (Zhang and Yu, 2008) and (Zhang et al., 2006).
Autor en correspondencia. pmillan@cartuja.us.es
Bibliografía
1. Azimi-Sadjadi, B., December 2003. Stability of networked control systems in the presence of packet losses. In: Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, Hawaii, USA, pp. 676-681.
2. Branicky MS, Borkar VS, Mitter SK. A unified framework for hybrid control: model and optimal control theory. IEEE Trans. on Automatic Control. 1998; 43(1):31-45.
3. Delfour MC, McCalla C, Mitter SK. Stability and infinite-time quadratic cost problem for linear hereditary di_erential systems. SIAM Journal on Control and Optimization. 1975; 13(1):48-88.
4. Dormido S, Sánchez J, Kofman E. Muestreo, control y comunicación basado en eventos. RIAI Revista Iberoamericana de Automática e Informática Industrial. 2008; 5(1):5-26.
5. El Ghaoui L, Oustry F, AitRami M. A cone complementary linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control. 1997; 42(8):1171-6.
6. Esfahani SH, Moheimani SOR, Petersen IR. LMI approach to suboptimal guaranteed cost control for uncertain time-delay systems. IEE Proceedings Control Theory and Applications. 1998; 145(6):491-8.
7. Gupta V, Hassibi B, Murray RM. Optimal LQG control across packet-dropping links. Systems and Control Letters. 2007; 56(6):439-46.
8. Hale, J.C., Verduyn Lunel, S.M., 1993. Introduction of functional di_erential equations. Springer, New York.
9. Hespanha J, Naghshtabrizi P, Xu Y. A survey of recent results in networked control systems. Proceedings of the IEEE, special edition. 2007; 95(1):138-62.
10. Hokayem, P.F., Abdallah, C.T., June 2004. Inherent issues in networked control systems: a survey. In: Proceedings of the American Control Conference. Boston, Massachusetts, USA, pp. 4897-4902.
11. Jiang X, Han QL. New stability criteria for linear systems with interval time-varying delay. Automatica. 2008; 44(10):2680-5.
12. Jiang X, Han QL, Liu S, Xue A. A new H1 stabilization criterion for networked control systems. IEEE Transactions on Automatic Control. 2008; 53(4):1025-32.
13. Kharatishvili GL. The maximum principle in the theory of optimal processes with delay (in russian). Dokl. Akad. Nauk. SSSR. 1961; 136(1):39-42.
14. Kosmidou OI, Boutalis YS. A linear matrix inequality approach for guaranteed cost control of systems with state and input delays. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans. 2006; 36(5):936-42.
15. Krasovskii N. On analytic design of optimal controllers for systems with time delay. Prikl. matem. i mekh. 1962; 26(1):39-51.
16. Mahmoud, M.S., 2000. Robust Control and Filtering for Time-delay Systems. Marcel Dekker, Inc., New York.
17. Meng X, Lam J, Gao H. Network-based H1 control for stochastic systems. International Journal of Robust and Nonlinear Control. 2009; 19(3):295-312.
18. Mikheev YV, Sobolev VA, Fridman E. Asymptotic analysis of digital control systems. Automatic and Remote Con**trol. 1988; 49:1175-80.
19. Naghshtabrizi, P., Hespanha, J., December 2005. Designing an observer-based controller for a network control system. In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville, Spain, pp. 848-853.
20. Nikolakopoulos G, Panousopoulou A, Tzes A. Experimental controller tuning and QoS optimization of a wireless transmission scheme for realtime remote control applications. Control Engineering Practice. 2008; 16(3):333-46.
21. Ross DW, Flugge-Lotz I. An optimal control problem for systems with di_erential di_erence equation dynamics. SIAM Journal On Control and Optimization. 1969; 7(4):609-23.
22. Salt J, Casanova V, Cuenca A, Pizá R. Sistemas de control basados en red. modelado y diseño de estructuras de control. RIAI Revista Iberoamericana de Automática e Informática Industrial. 2008; 5(3):5-20.
23. Shao H. New delay-dependent stability criteria for systems with interval delay. Automatica. 2009; 45(3):744-9.
24. Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Sastry, S., December 2005. An LQG optimal linear controller for control systems with packet losses. In: 44th IEEE Conference on Decision and Control and the European Control Conference. Sevilla, Spain, pp. 458-463.
25. Tatikonda S, Mitter S. Control under communication constraints. IEEE Transactions on Automatic Control. 2004; 49(7):1056-68.
26. Xiong J, Lam J. Stabilization of linear systems over networks with bounded packet loss. Automatica. 2007; 43(1):80-7.
27. Xu S, Lam J. On equivalence and e_ciency of certain stability criteria for time-delay systems. IEEE Transactions on Automatic Control. 2007; 52(1):95-101.
28. Xu S, Lam J. A survey of linear matrix inequality techniques in stability analysis of delay systems. International Journal of Systems Science. 2008; 39(12):1095-113.
29. Yue D, Han QL, Lam J. Network-based robust H1 control of systems with uncertainty. Automatica. 2005; 41(6):999-1007.
30. Zampieri, S., July 2008. Trends in networked control systems. In: Proceedings of the 17th World Congress IFAC. Seoul, Korea, pp. 2886-2894.
31. Zhang D, Yu L. Equivalence of some stability criteria for linear timedelay systems. Applied Mathematics and Computation. 2008; 202(1):395-400.
32. Zhang HS, Duan G, Xie L. Linear quadratic regulation for linear time varying systems with multiple input delays. Automatica. 2006; 42(9):1465-76.
Millán, Pabloa; Orihuela, Luisa; Vivas, Carlosa; Rubio, Francisco R.a
aDepartamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n, Isla de la Cartuja, Sevilla, España
