zbMATH — the first resource for mathematics

Observer design for systems with multivariable monotone nonlinearities. (English) Zbl 1157.93330
Summary: Globally convergent observers are designed for a class of systems with multivariable nonlinearities. The approach is to represent the observer error system as the feedback interconnection of a linear system and a state-dependent multivariable nonlinearity. We first extend an earlier design (Automatica 37 (12) (2001) 1923) to multivariable nonlinearities, satisfying an analog of the scalar nondecreasing property. Next, we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system. This relaxed design renders the feasibility conditions less restrictive, and widens the applicability of the observer, as illustrated with examples. Finally, output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters.

93B07 Observability
93B50 Synthesis problems
Full Text: DOI
[1] Aamo, O.M.; Arcak, M.; Fossen, T.I.; Kokotović, P.V., Global output tracking control of a class of euler – lagrange systems with monotonic nonlinearities in the velocities, Internat. J. control, 74, 7, 649-658, (2001) · Zbl 1017.93096
[2] M. Arcak, A global separation theorem for a new class of nonlinear observers, Proceedings of the 41st Conference on Decision and Control, Las Vegas, Nevada, December 2002, pp. 676-681.
[3] M. Arcak, H. Gorgun, L.M. Pedersen, S. Varigonda, An adaptive observer design for fuel cell hydrogen estimation, Proceedings of the American Control Conference, Denver, Colorado, June 2003, to appear.
[4] Arcak, M.; Kokotović, P., Feasibility conditions for circle criterion design, Systems control lett., 42, 405-412, (2001) · Zbl 0974.93049
[5] Arcak, M.; Kokotović, P., Nonlinear observersa circle criterion design and robustness analysis, Automatica, 37, 12, 1923-1930, (2001) · Zbl 0996.93010
[6] Arcak, M.; Kokotović, P., Observer-based control of systems with slope-restricted nonlinearities, IEEE trans. automat. control, 4, 7, 1146-1151, (2001) · Zbl 1014.93033
[7] A. Howell, J.K. Hedrick, Nonlinear observer design via convex optimization, in: Proceedings of the American Control Conference, Anchorage, Alaska, 2002, pp. 2088-2093.
[8] Kazantzis, N.; Kravaris, C., Nonlinear observer design using Lyapunov’s auxiliary theorem, Systems control lett., 34, 241-247, (1998) · Zbl 0909.93002
[9] Khalil, H.K., Nonlinear systems, (1996), Prentice-Hall Englewood Cliffs, NJ · Zbl 0626.34052
[10] Khalil, H.K., High-gain observers in nonlinear feedback control, (), 249-268 · Zbl 0942.93038
[11] Krener, A.J.; Isidori, A., Linearization by output injection and nonlinear observers, Systems control lett., 3, 47-52, (1983) · Zbl 0524.93030
[12] Lohmiller, J.-J.; Slotine, W., On contraction analysis for nonlinear systems, Automatica, 34, 683-696, (1998) · Zbl 0934.93034
[13] Ortega, J.M.; Rheinboldt, W.C., Interative solution of nonlinear equations in several variables, (2000), SIAM Philadelphia · Zbl 0949.65053
[14] L. Praly, M. Arcak, On certainty-equivalence design of nonlinear observer-based controllers, Proceedings of the 41st Conference on Decision and Control, Las Vegas, Nevada, December 2002, pp. 1485-1490.
[15] Raghavan, S.; Hedrick, J.K., Observer design for a class of nonlinear systems, Internat. J. control, 59, 515-528, (1994) · Zbl 0802.93007
[16] Thau, F.E., Observing the state of non-linear dynamic systems, Internat. J. control, 17, 471-479, (1973) · Zbl 0249.93006
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.