Abstract
In this paper the inverse optimal stabilization problem is solved for nonlinear nonaffine control discrete-time systems which are globally stable when uncontrolled. Stabilizing feedback laws and nonquadratic cost functionals are constructed. The result is applied to feedforward systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B.D.O. Anderson and J.B. Moore: Linear Optimal Control, Prentice-Hall, Englewood Cliffs, NJ, 1971.
R.A. Freeman and P.V. Kokotovic: Inverse optimality in robust stabilization, SIAM Journal on Control and Optimization, vol. 34, pp. 1365–1391, 1996.
R.A. Freeman and P.V. Kokotovic: Robust Nonlinear Control Design, Birkhauser, Boston, 1996.
W.M. Haddad, V. Chellaboina and J.L. Fausz: Optimal Nonlinear Disturbance Rejection Control for Nonlinear Cascade Systems, Int. J. Contr., 68 (1997) 997–1018.
M. Jankovic, R. Sepulchre and P.V. Kokotovic: Global stabilization of an enlarged class of cascade nonlinear systems. IEEE Trans. on Automatic Control, vol.41, no.12, pp.1723–1735, 1996.
V. Jurdjevic, J.P. Quinn: Controllability and stability. J. Differential Equations, vol.4, pp. 381–389, 1978.
R.E. Kalman: When is a linear control systtem optimal? Trans. ASME Ser. D: J. Basic En., vol. 86, pp. 1–10, 1964.
M. Krstić and Zhong-Hua Li: Inverse optimal design of input-to-state stabilizing nonlinear controllers, Preprint 1997.
Zhong-Hua Li and M. Krstić: Optimal design of adaptive tracking controllers for nonlinear systems, Proc. ACC, Albuquerque, New Mexico, 1997.
Wei Lin: Further results on global stabilization of discrete-time nonlinear systems. Systems & Control Letters, 29, 51–59, 1996.
Wei Lin and C. Byrnes: Passivity and Absolute Stabilization of a Class of Discrete-time Nonlinear Systems. Automatica, Vol. 31.No.2, pp. 263–267, 1995.
F. Mazenc: Stabilization of Feedforward Systems Approximated by a Nonlinear Chain of Integrators. Systems & Control Letters 32 (1997) 223–229.
F. Mazenc and L. Praly: Adding an integration and Global asymptotic stabilization of feedforward systems. IEEE Trans. on Automatic Control, vol.41,no.11, pp.1559–1578, 1996.
F. Mazenc and H. Nijmeijer: Forwarding in discrete-time nonlinear systems. Int. J. Control, 1998, vol. 71,No.5, pp. 823–835.
F. Mazenc, R. Sepulchre and M. Jankovic: Lyapunov functions for stable cascades and applications to global stabilization. 36th CDC conference, San Diego, 1997 and to appear in IEEE Trans. Automatic Control.
P.J. Moylan and B.D. Anderson: Nonlinear regulator theory and an inverse optimal control problem. IEEE Trans. Automatic Control, vol. 18, pp. 460–465, 1973.
R. Sepulchre, M. Jankovic and P.V. Kokotovic, Constructive Nonlinear Control, Springer-Verlag, 1997.
H.J. Susmann, E.D. Sontag and Y. Yang: A general result on the stabilization of linear systems using bounded control. IEEE Trans. on Automatic Control, vol. 39, pp. 2411–2425, 1994.
A. Teel: Feedback Stabilization: Nonlinear Solutions to Inherently Nonlinear Problems. PhD Dissertation, University of California, Berkeley, 1992.
A. Teel: On L 2 performance induced by feedbacks with multiple saturations. ESAIM: Control, Optimisation and Clculus of Variations, vol. 1, pp. 225–240, Spetembre 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag London Limited
About this paper
Cite this paper
Ahmed-Ali, T., Mazenc, F., Lamnabhi-Lagarrigue, F. (1999). Disturbance attenuation for discrete-time feedforward nonlinear systems. In: Aeyels, D., Lamnabhi-Lagarrigue, F., van der Schaft, A. (eds) Stability and Stabilization of Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 246. Springer, London. https://doi.org/10.1007/1-84628-577-1_1
Download citation
DOI: https://doi.org/10.1007/1-84628-577-1_1
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-638-7
Online ISBN: 978-1-84628-577-6
eBook Packages: Springer Book Archive