zbMATH — the first resource for mathematics

Robust output feedback control of quasi-linear parabolic PDE systems. (English) Zbl 0915.93025
Summary: This paper proposes a methodology for the synthesis of nonlinear robust output feedback controllers for systems of quasi-linear parabolic partial differential equations with time-varying uncertain variables. The method is successfully applied to a typical diffusion-reaction process with uncertainty.

93C20 Control/observation systems governed by partial differential equations
93B52 Feedback control
93D21 Adaptive or robust stabilization
Full Text: DOI
[1] Balas, M.J., Feedback control of linear diffusion processes, Int. J. control, 29, 523-533, (1979) · Zbl 0398.93027
[2] Balas, M.J., Stability of distributed parameter systems with finite-dimensional controller-compensators using singular perturbations, J. math. anal. appl., 99, 80-108, (1984) · Zbl 0553.93048
[3] J.A. Burns, B.B. King, Optimal sensor location for robust control of distributed parameter systems, Proc. 33rd IEEE Conf. Decision and Control, Orlando, FL, 1994, pp. 3965-3970.
[4] J.A. Burns, Y. Ou, Feedback control of the driven cavity problem using LQR designs, Proc. 33rd IEEE Conf. Decision and Control, Orlando, FL, 1994, pp. 289-294.
[5] C.I. Byrnes, Adaptive stabilization of infinite dimensional linear systems, Proc. 26th IEEE Conf. Decision and Control, Los Angeles, CA, 1987, pp. 1435-1440.
[6] C.I. Byrnes, D.S. Gilliam, V.I. Shubov, Global lyapunov stabilization of a nonlinear distributed parameter system, Proc. 33rd IEEE Conf. Decision and Control, Orlando, FL, 1994, pp. 1769-1774.
[7] C.I. Byrnes, D.S. Gilliam, V.I. Shubov, On the dynamics of boundary controlled nonlinear distributed parameter systems, Proc. Symp. Nonlinear Control Systems Design’95, Tahoe City, CA, 1995, pp. 913-918.
[8] Christofides, P.D., Robust control of parabolic PDE systems, Chem. eng. sci., 53, 2949-2965, (1998)
[9] Christofides, P.D.; Daoutidis, P., Feedback control of hyperbolic PDE systems, A.i.ch.e. j., 42, 3063-3086, (1996)
[10] Christofides, P.D.; Daoutidis, P., Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds, J. math. anal. appl., 216, 398-420, (1997) · Zbl 0890.93051
[11] Christofides, P.D.; Daoutidis, P., Robust control of hyperbolic PDE systems, Chem. eng. sci., 53, 85-105, (1998)
[12] Curtain, R.F., Finite-dimensional compensator design for parabolic distributed systems with point sensors and boundary input, IEEE trans. automat. control, 27, 98-104, (1982) · Zbl 0477.93039
[13] R.F. Curtain, Disturbance decoupling for distributed systems by boundary control, Proc. 2nd Internat. Conf. Control Theory for Distributed Parameter Systems and Applications, Vorau, Austria, 1984, pp. 109-123.
[14] Curtain, R.F., Invariance concepts in infinite dimensions, SIAM J. control optim., 24, 1009-1030, (1986) · Zbl 0602.93037
[15] Curtain, R.F.; Glover, K., Robust stabilization of infinite dimensional systems by finite dimensional controllers, Systems control lett., 7, 41-47, (1986) · Zbl 0601.93044
[16] M.A. Demetriou, Model reference adaptive control of slowly time-varying parabolic systems, Proc. 33rd IEEE Conf. Decision and Control, Orlando, FL, 1994, pp. 775-780.
[17] Foias, C.; Sell, G.R.; Titi, E.S., Exponential tracking and approximation of inertial manifolds for dissipative equations, J. dynamics and differential equations, 1, 199-244, (1989) · Zbl 0692.35053
[18] Gauthier, J.P.; Xu, C.Z., H∞-control of a distributed parameter system with non-minimum phase, Int. J. control, 53, 45-79, (1989) · Zbl 0724.93028
[19] A. Isidori, Nonlinear Control Systems: An Introduction, 2nd ed., Springer, Berlin-Heidelberg, 1989. · Zbl 0569.93034
[20] Jacobson, C.A.; Nett, C.N., Linear state-space systems in infinite-dimensional space: the role and characterization of joint stabilizability/detectability, IEEE trans. automat. control, 33, 541-551, (1988) · Zbl 0645.93025
[21] S. Kang, K. Ito, A feedback control law for systems arising in fluid dynamics, Proc. 30th IEEE Conf. Decision and Control, Tampa, AZ, 1992, pp. 384-385.
[22] B.B. King, Y. Qu, Nonlinear dynamic compensator design for flow control in a driven cavity, Proc. 34th IEEE Conf. Decision and Control, New Orleans, LA, 1995, pp. 3741-3746.
[23] P.V. Kokotovic, H.K. Khalil, J. O’Reilly, Singular Perturbations in Control: Analysis and Design, Academic Press, London, 1986.
[24] Sano, H.; Kunimatsu, N., An application of inertial manifold theory to boundary stabilization of semilinear diffusion systems, J. math. anal. appl., 196, 18-42, (1995) · Zbl 0844.93065
[25] B. van Keulen, H∞-Control for Distributed Parameter Systems: A State-Space Approach, Birkhauser, Boston, 1993. · Zbl 0788.93018
[26] Wen, J.T.; Balas, M.J., Robust adaptive control in Hilbert space, J. math. anal. appl., 143, 1-26, (1989) · Zbl 0701.93086
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.