Continuous Adaptive Robust Control for Nonlinear Uncertain Systems
We consider nonlinear uncertain systems such that a
priori information of the uncertainties is not available. For such
systems, we assume that the upper bound of the uncertainties is
represented as a Fredholm integral equation of the first kind and we
propose an adaptation law that is capable of estimating the upper
bound and design a continuous robust control which renders nonlinear
uncertain systems ultimately bounded.
[1] Gutman, S., "Uncertain dynamical systems - A Lyapunov min-max
approach,” IEEE Trans. on Automatic Control, Vol. 24, No. 3,
pp.437-443(1979).
[2] Corless, M. J., and Leitman, G., "Continuous state feedback
guaranteeing uniform ultimate boundedness for uncertain dynamic
systems,” IEEE Trans. on Automatic Control, Vol. 26, No. 5,
pp.1139-1144(1981).
[3] Barmish, B. R., Corless, M. J., and Leitmann, G., "A new class of
stabilizing controllers for uncertain dynamical systems,” SIAM J. on
Control and Optimization, Vol. 21, No. 2, pp.246-255(1983).
[4] Chen, Y. H., "Design of robust controllers for uncertain dynamical
systems,” IEEE Trans. on Automatic Control, Vol. 33, No. 5,
pp.487-491(1988).
[5] Chen, Y. H., "Robust control system design: non-adaptive and
adaptive,” Int. J. of Control, Vol. 51, No. 6, pp.1457-1477(1990).
[6] Yoo, D. S., and Chung, M. J., "A Variable structure control with simple
adaptation laws for upper bounds on the norm of the uncertainties,”
IEEE Trans. on Automatic Control, Vol. 37, No. 6, pp.860-865(1992).
[7] Brogliato, B., and Trofino Neto, A., "Practical stabilization of a class of
nonlinear systems with partially known uncertainties,” Automatica, Vol.
31, No. 1, pp.145-150(1995).
[8] Wu, H., "Continuous adaptive robust controllers guaranteeing uniform
ultimate boundedness for uncertain nonlinear system,” Int. J. of Control,
Vol. 72, No. 2, pp.115-122(1999).
[9] Arfken, G., and Weber, H., Mathematical methods for physicists, New
York: Academic Press, N.Y., pp.725- 748 (1970).
[10] Messner, W., Horowitz, R., Kao, W.-W., and Boals, M., "A New
Adaptive Learning Rule,” IEEE Trans. on Automatic Control, Vol. 36,
No. 2, pp.188-197(1991).
[1] Gutman, S., "Uncertain dynamical systems - A Lyapunov min-max
approach,” IEEE Trans. on Automatic Control, Vol. 24, No. 3,
pp.437-443(1979).
[2] Corless, M. J., and Leitman, G., "Continuous state feedback
guaranteeing uniform ultimate boundedness for uncertain dynamic
systems,” IEEE Trans. on Automatic Control, Vol. 26, No. 5,
pp.1139-1144(1981).
[3] Barmish, B. R., Corless, M. J., and Leitmann, G., "A new class of
stabilizing controllers for uncertain dynamical systems,” SIAM J. on
Control and Optimization, Vol. 21, No. 2, pp.246-255(1983).
[4] Chen, Y. H., "Design of robust controllers for uncertain dynamical
systems,” IEEE Trans. on Automatic Control, Vol. 33, No. 5,
pp.487-491(1988).
[5] Chen, Y. H., "Robust control system design: non-adaptive and
adaptive,” Int. J. of Control, Vol. 51, No. 6, pp.1457-1477(1990).
[6] Yoo, D. S., and Chung, M. J., "A Variable structure control with simple
adaptation laws for upper bounds on the norm of the uncertainties,”
IEEE Trans. on Automatic Control, Vol. 37, No. 6, pp.860-865(1992).
[7] Brogliato, B., and Trofino Neto, A., "Practical stabilization of a class of
nonlinear systems with partially known uncertainties,” Automatica, Vol.
31, No. 1, pp.145-150(1995).
[8] Wu, H., "Continuous adaptive robust controllers guaranteeing uniform
ultimate boundedness for uncertain nonlinear system,” Int. J. of Control,
Vol. 72, No. 2, pp.115-122(1999).
[9] Arfken, G., and Weber, H., Mathematical methods for physicists, New
York: Academic Press, N.Y., pp.725- 748 (1970).
[10] Messner, W., Horowitz, R., Kao, W.-W., and Boals, M., "A New
Adaptive Learning Rule,” IEEE Trans. on Automatic Control, Vol. 36,
No. 2, pp.188-197(1991).
@article{"International Journal of Electrical, Electronic and Communication Sciences:66058", author = "Dong Sang Yoo", title = "Continuous Adaptive Robust Control for Nonlinear Uncertain Systems", abstract = "We consider nonlinear uncertain systems such that a
priori information of the uncertainties is not available. For such
systems, we assume that the upper bound of the uncertainties is
represented as a Fredholm integral equation of the first kind and we
propose an adaptation law that is capable of estimating the upper
bound and design a continuous robust control which renders nonlinear
uncertain systems ultimately bounded.
", keywords = "Adaptive Control, Estimation, Fredholm Integral, Uncertain System. ", volume = "8", number = "1", pages = "13-5", }