×

zbMATH — the first resource for mathematics

Adaptive robust control of uncertain systems with measurement noise. (English) Zbl 0766.93045
Summary: A class of dynamical with time-varying uncertainty is considered. The nominal portion (i.e. the portion without uncertainty) of the system is stabilizable. The uncertainty is either assumed to satisfy the matching condition or is close to matching. Moreover, the uncertainty is to be cone-bounded. The bound is, however, unknown. The control design is only based on the deterministic properties related to the bound of uncertainty. The feedback information is the state with measurement noise.

MSC:
93C99 Model systems in control theory
93B35 Sensitivity (robustness)
93C35 Multivariable systems, multidimensional control systems
93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
Keywords:
time-dependent
PDF BibTeX Cite
Full Text: DOI
References:
[1] Åström, K.J.; Wittenmark, B., ()
[2] Barmish, B.R.; Corless, M.; Leitmann, G., A new class of stabilizing controllers for uncertain dynamical systems, SIAM J. control optimization, 21, 246-255, (1982) · Zbl 0503.93049
[3] Barmish, B.R.; Leitmann, G., On ultimate boundedness control of uncertain systems in the absence of matching conditions, IEEE trans. aut. control, AC-27, 153-158, (1982) · Zbl 0469.93043
[4] Chen, Y.H., On the deterministic performance of uncertain dynamical systems, Int. J. control, 43, 1557-1579, (1986) · Zbl 0606.93028
[5] Chen, Y.H., Design of robust controllers for uncertain dynamical systems, IEEE trans. aut. control, AC-33, 487-491, (1988) · Zbl 0638.93053
[6] Chen, Y.H., Modified adaptive robust control system design, Int. J. control, 49, 1869-1882, (1989) · Zbl 0683.93027
[7] Chen, Y.H.; Leitmann, G., Robustness of uncertain systems in the absence of matching assumptions, Int. J. control, 45, 1527-1542, (1987) · Zbl 0623.93023
[8] Coddington, E.A.; Levinson, N., ()
[9] Corless, M.J.; Leitmann, G., Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE trans. aut. control, 26, 1139-1143, (1981) · Zbl 0473.93056
[10] Corless, M.; Leitmann, G., Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds, J. optimization theory applications, 41, 155-168, (1983) · Zbl 0497.93028
[11] Corless, M.; Leitmann, G., Adaptive control for uncertain dynamical systems, () · Zbl 0556.93042
[12] Daniel, R.W.; Kouvaritakis, B., A new robust stability criterion for linear and nonlinear multivariable feedback systems, Int. J. control, 41, 1349-1379, (1985) · Zbl 0575.93058
[13] Desoer, C.A.; Vidyasagar, M., ()
[14] Doyle, J.C., Achievable performance in multivariable feedback systems, (), 250-251
[15] Fu, L.-C.; Bodson, M.; Sastry, S.S., New stability theorems for averaging and their application to the convergence analysis of adaptive identification and control schemes, ()
[16] Hale, J.K., ()
[17] Ioannou, P.A.; Kokotovic, P.V., ()
[18] Kantor, J.C.; Andres, R.P., Characterization of ‘allowable perturbations’ for robust stability, IEEE trans. aut. control, AC-28, 107-109, (1983) · Zbl 0502.93056
[19] Kosut, R.L., Analysis of performance robustness for uncertain multivariable systems, (), 1289-1294
[20] Kreisselmeier, G.; Anderson, B.D.O., Robust model reference adaptive control, IEEE trans. aut. control, AC-31, 127-133, (1986) · Zbl 0583.93039
[21] Lehtomaki, N.A.; Sandell, N.R.; Athans, M., Robustness results in linear quadratic Gaussian based multivariable control design, IEEE trans. aut. control, AC-26, 75-92, (1981) · Zbl 0459.93024
[22] Leitmann, G., On the efficacy of nonlinear control in uncertain systems, J. dynamic systems, measurement and control, 10, 95-102, (1981) · Zbl 0473.93055
[23] Lunze, J., Robustness analysis of control systems by means of a structured uncertainty description, Foundations of control engineering, 10, 201-213, (1986) · Zbl 0598.93018
[24] Molander, P.; Willems, J.C., Synthesis of state feedback control laws with specified gain and phase margin, IEEE trans. aut. control, AC-25, 928-931, (1980) · Zbl 0461.93046
[25] Narendra, K.S.; Annaswamy, A.M., A new adaptive law for robust adaptive control without persistent excitation, IEEE trans. aut. control, 32, 134-145, (1987) · Zbl 0617.93035
[26] Owens, D.H.; Chotai, A., On eigenvalues, eigenvectors and singular values in robust stability analysis, International J. control, 40, 285-296, (1984) · Zbl 0551.93056
[27] Patel, R.V.; Toda, M., Quantitative measures of robustness for multivariable systems, () · Zbl 0422.93046
[28] Peterson, B.B.; Narendra, K.S., Bounded error adaptive control, IEEE trans. aut. control, AC-27, 1161-1168, (1982) · Zbl 0497.93026
[29] Safonov, M.G., ()
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.