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Synthesis of min-max strategies. (English) Zbl 0548.93033

We present the min-max control for a class of nonlinear uncertain dynamical systems. In particular, we discuss the problems of tracking and adaptive adjustment of the control effort.

MSC:

93B50 Synthesis problems
93C10 Nonlinear systems in control theory
93C40 Adaptive control/observation systems
93B35 Sensitivity (robustness)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
Full Text: DOI

References:

[1] Gutman, S., andLeitmann, G.,On a Class of Linear Differential Games, Journal of Optimization Theory and Applications, Vol. 17, Nos. 5-6, 1975. · Zbl 0296.90054
[2] Gutman, S., andLeitmann, G.,Stabilizing Control for Linear Systems with Bounded Parameter and Input Uncertainty, Proceedings of the 7th IFIP Conference on Optimization Techniques, Nice, France, Springer-Verlag, Berlin, Germany, 1976. · Zbl 0334.93030
[3] Gutman, S.,Uncertain Dynamical Systems: A Lyapunov Min-Max approach, IEEE Transactions on Automatic Control, Vol. AC-24, pp. 437-443, 1979. · Zbl 0416.93076 · doi:10.1109/TAC.1979.1102073
[4] Leitmann, G.,On the Efficacy of Nonlinear Control in Uncertain Linear Systems, Journal of Dynamic Systems, Measurement, and Control, Vol. 103, pp. 95-102, 1981. · Zbl 0473.93055 · doi:10.1115/1.3139661
[5] Gutman, S., andPalmor, Z.,Properties of Min-Max Controllers in Uncertain Dynamical Systems, SIAM Journal on Control and Optimization, Vol. 20, pp. 850-861, 1982. · Zbl 0504.49024 · doi:10.1137/0320060
[6] Corless, M., andLeitmann, G.,Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems, IEEE Transactions on Automatic Control, Vol. AC-26, pp. 1134-1144, 1981. · Zbl 0473.93056
[7] Corless, M., andLeitmann, G.,Adaptive Control of Systems Containing Uncertain Functions and Unknown Functions with Uncertain Bounds, Journal of Optimization Theory and Applications, Vol. 41, pp. 155-168, 1983. · Zbl 0497.93028 · doi:10.1007/BF00934441
[8] Ambrosino, G., Celentano, G., andGarofalo, F.,Robust Model Tracking for a Class of Nonlinear Plants, IEEE Transactions on Automatic Control, Vol. AC-30, pp. 275-279, 1985. · Zbl 0558.93068 · doi:10.1109/TAC.1985.1103929
[9] Bengtsson, G.,Output Regulation and Internal Models: A Frequency Domain Approach, Automatica, Vol. 13, pp. 333-345, 1977. · Zbl 0359.93009 · doi:10.1016/0005-1098(77)90016-4
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