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Keywords:
nonlinear systems; observer design; backstepping; counter-convecting transport dynamics
nonlinear systems; observer design; backstepping; counter-convecting transport dynamics
Summary:
Observer design for ODE-PDE cascades is studied where the finite-dimension ODE is a globally Lipschitz nonlinear system, while the PDE part is a pair of counter-convecting transport dynamics. One major difficulty is that the state observation only rely on the PDE state at the terminal boundary, the connection point between the ODE and the PDE blocs is not accessible to measure. Combining the backstepping infinite-dimensional transformation with the high gain observer technology, the state of the ODE subsystem and the state of the pair of counter-convecting transport dynamics are estimated. It is shown that the observer error is asymptotically stable. A numerical example is given to illustrate the effectiveness of the proposed method.
References:
[1] Andrieu, V., Praly, L.: On the existence of Kazantzis-Kravaris/Luenberger observers. SIAM J. Control Optim. 45 (2006), 432-456. DOI 10.1137/040617066 | MR 2246084
[2] Cai, X., Krstic, M.: Control of discrete-time nonlinear systems actuated through counterconvecting transport dynamics. J. Control Decision 1 (2014), 34-50. DOI 10.1080/23307706.2014.885290
[3] Cai, X., Krstic, M.: Nonlinear control under wave actuator dynamics with time- and state-dependent moving boundary. Int. J. Robust. Nonlinear Control 25 (2015), 222-253. DOI 10.1002/rnc.3083 | MR 3293094 | Zbl 1305.93167
[4] Cai, X., Lin, Y., Liu, L.: Universal stabilisation design for a class of non-linear systems with time-varying input delays. IET Control Theory Appl. 9 (2015), 1481-1490. DOI 10.1049/iet-cta.2014.1085 | MR 3381705
[5] Coron, J., Vazquez, R., Krstic, M., Bastin, G.: Local exponential H2 stabilization of a 2x2 quasilinear hyperbolic system using backstepping. SIAM J. Control Optim. 51 (2013), 2005-2035. DOI 10.1137/120875739 | MR 3049647
[6] Curro, C., Fusco, D., Manganaro, N.: A reduction procedure for generalized Riemann problems with application to nonlinear transmission lines. J. Physics A: Math. Theory 44 (2011), 335205. DOI 10.1088/1751-8113/44/33/335205 | MR 2822118 | Zbl 1223.35220
[7] Santos, V. Dos, Prieur, C.: Boundary control of open channels with numerical and experimental validations. IEEE Trans. Control System Technol. 16 (2008), 1252-1264. DOI 10.1109/tcst.2008.919418
[8] Fridman, L., Shtessel, Y., Edwards, C., Yan, X. G.: Higer-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. Int. J. Robust Nonlinear Control 18 (2008), 399-412. DOI 10.1002/rnc.1198 | MR 2392130
[9] Goatin, P.: The Aw-Rascle vehicular traffic flow model with phase transitions. Math. Computer Modeling 44 (2006), 287-303. DOI 10.1016/j.mcm.2006.01.016 | MR 2239057 | Zbl 1134.35379
[10] Gugat, M., Dick, M.: Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Math. Control Related Fields 1 (2011), 469-491. DOI 10.3934/mcrf.2011.1.469 | MR 2871937
[11] Krstic, M.: Compensating a string PDE in the actuation or sensing path of an unstable ODE. Systems Control Lett. 54 (2009), 1362-1368. DOI 10.1109/tac.2009.2015557 | MR 2532631
[12] Krstic, M.: Compensating actuator and sensor dynamics governed by diffusion PDEs. Systems Control Lett. 58 (2009), 372-377. DOI 10.1016/j.sysconle.2009.01.006 | MR 2512493 | Zbl 1159.93024
[13] Krstic, M., Bekiaris-Liberis, N.: Nonlinear stabilization in infinite dimension. Ann. Rev. Control 37 (2013), 220-231. DOI 10.1016/j.arcontrol.2013.09.002
[14] Krstic, M., Smyshlyaev, A.: Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays. Systems Control Lett. 57 (2008), 750-758. DOI 10.1016/j.arcontrol.2013.09.002 | MR 2446460 | Zbl 1153.93022
[15] Meglio, F. Di, Krstic, M., Vazquez, R., Petit, N.: Backstepping stabilization of an underactuated $3 \times 3$ linear hyperbolic system of fluid flow transport equations. In: Proc. American Control Conference, Montreal 2012, pp. 3365-3370. DOI 10.1109/acc.2012.6315422
[16] Meglio, F. Di, Vazquez, R., Krstic, M.: Stabilization of a system of n + 1 coupled first-order hyperbolic linear PDEs with a single boundary input. IEEE Trans. Automat. Control 58 (2013), 3097-3111. DOI 10.1109/tac.2013.2274723 | MR 3152271
[17] Shim, H., Son, Y. I., Seo, J. H.: Semi-global observer for multi-output nonlinear system. System Control Lett. 42 (2001), 233-244. DOI 10.1016/s0167-6911(00)00098-0 | MR 2007052
[18] Vazquez, R., Krstic, M.: Control of 1-D parabolic PDEs with Volterra nonlinearities. Part I: Design. Automatica 44 (2008), 2778-2790. DOI 10.1016/j.automatica.2008.04.013 | MR 2527199
[19] Vazquez, R., Krstic, M.: Control of 1-D parabolic PDEs with Volterra nonlinearities, Part II: Analysis. Automatica 44 (2008), 2791-2803. DOI 10.1016/j.automatica.2008.04.007 | MR 2527200
[20] Wu, H., Wang, J.: Observer design and output feedback stabilization for nonlinear multivariable systems with diffusion PDE-governed sensor dynamics. Nonlinear Dyn. 72 (2013), 615-628. DOI 10.1007/s11071-012-0740-4 | MR 3046917 | Zbl 1268.93124
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