zbMATH — the first resource for mathematics

On the state observation and output feedback problems for nonlinear uncertain dynamic systems. (English) Zbl 0752.93021
Summary: We examine the problems of state observation and state trajectory control by output feedback for the class of nonlinear systems in A. Steinberg and M. Corless [IEEE Trans. Autom. Control AC-30, 1025- 1027 (1985; Zbl 0565.93047)] and Y. H. Chen [Int. J. Syst. Sci. 21, No. 5, 803-814 (1990; Zbl 0717.93007)]. We begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is Globally Exponentially Stable (GES). We then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the GES sense. Specific time-varying bounds on the observation error and the state trajectory are also developed; revealing how the corresponding observer or control parameters can be adjusted to improve the system performance.

93B35 Sensitivity (robustness)
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
[1] Baumann, W.; Rugh, W., Feedback control of nonlinear systems by extended linearization, IEEE trans. automat. control, 31, 1, 40-46, (1986) · Zbl 0582.93031
[2] Bestle, D.; Zeitz, M., Canonical form observer design for non-linear time-variable systems, Internat. J. control, 38, 2, 419-431, (1983) · Zbl 0521.93012
[3] Chen, Y., Adaptive robust observers for non-linear uncertain systems, Internat. J. systems sci., 21, 5, 803-814, (1990) · Zbl 0717.93007
[4] Corless, M.; Leitmann, G., Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE trans. automat. controls, 26, 1139-1143, (1981) · Zbl 0473.93056
[5] Kailath, T., Linear systems, (1980), Prentice Hall Englewood Cliffs, NJ · Zbl 0458.93025
[6] Kou, S.; Elliott, D.; Tarn, T., Exponential observers for nonlinear dynamic systems, Inform. and control, 29, 3, 204-216, (1976) · Zbl 0319.93049
[7] Krener, A.; Respondek, W., Nonlinear observers with linearizable error dynamics, SIAM J. control optim., 23, 2, 197-216, (1985) · Zbl 0569.93035
[8] Marino, R., High-gain feedback control in non-linear systems, Internat. J. control, 42, 6, 1369-1385, (1985) · Zbl 0609.93029
[9] Qu, Z.; Dawson, D., Continuous feedback control guaranteeing exponential stability for uncertain dynamic systems, IEEE conference on decision and control, (1991), to appear
[10] Slotine, J.; Li, W., Applied nonlinear control, (1991), Prentice Hall Englewood Cliffs, NJ
[11] Steinberg, A.; Corless, M., Output feedback stabilization of uncertain dynamical systems, IEEE trans. automat. control, 30, 1025-1027, (1985) · Zbl 0565.93047
[12] Thau, F., Observing the states of nonlinear dynamic systems, Internat. J. control, 17, 471-479, (1973) · Zbl 0249.93006
[13] Walcott, B.; Zak, S., State observation of nonlinear uncertain dynamical systems, IEEE trans. automat. control, 32, 2, 166-170, (1987) · Zbl 0618.93019
[14] Walcott, B., Nonlinear output stabilization of uncertain systems, (), 2253-2258
[15] Walcott, B.; Zak, S., Combined observer-controller synthesis for uncertain dynamical systems with applications, IEEE trans. systems man cybernet., 18, 1, 40-48, (1988)
[16] Vidyasagar, M., Nonlinear systems analysis, (1978), Prentice Hall Englewood Cliffs, NJ, New Jersey · Zbl 0407.93037
[17] Vostrikov, A.; Utkin, V.; Frantsuzova, G., Systems with state vector derivative in the control, Automat. and remote control, 6, 283-286, (1986) · Zbl 0504.93034
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.