Abstract
We consider a number of dynamical adaptive backstepping control algorithms for the class of observable non-minimum phase nonlinear continuous uncertain systems (triangular and non-triangular), as well as systems with disturbances which can be converted to the parametric semi-strict feedback form. Nonlinear, sliding and second-order sliding control laws are developed. Adaptive backstepping algorithms with tuning functions, and modular parameter identification approaches are presented. BACK, a Maple symbolic algebra package, has been developed as a tool for the design of dynamical adaptive nonlinear controllers for regulation and tracking tasks.
Preview
Unable to display preview. Download preview PDF.
References
Bartolini G., A. Ferrara, L. Giacomini and E. Usai (1996) A combined backstepping/second order sliding mode approach to control a class of nonlinear systems, Proc. IEEE International Workshop on Variable Structure Systems, Tokyo, Japan, 205–210
Bartolini, G., A. Ferrara and E. Usai (1997) Applications of a suboptimal discontinuous control algorithm for uncertain second order systems, Int. J. Robusk Nonlinear Control, 7, 299–320
Bartolini, G., A. Ferrara and E. Usai (1997) Output Tracking Control of Uncertain Nonlinear Second-Order Systems, Automatica, 33, 2203–2212
Bartolini, G., A. Ferrara and E. Usai (1998) Chattering avoidance by second-order sliding mode control, IEEE Trans. Automat. Contr., 43, 241–246
Blankenship, G. L., R. Ghanadan, H. G. Kwatny, C. LaVigna and V. Polyakov, (1995) Tools for integrated modelling, design, and nonlinear control, IEEE Control Systems Mag., 15, 65–79
Corless, M., and G. Leitmann (1981) Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamical systems, IEEE Trans. Automat. Contr., 26, 1139–1144
Freeman, R. A., and P. V. Kokotović (1996) Tracking controllers for systems linear in unmeasured states, Automatica, 32, 735–746
de Jager, B. (1996) Symbolic analysis and design for (nonaffiX-Mozilla-Status: 0009 systems, Proc. 13th IFAC World Congress, San Francisco, F, 289–294)
Glumineau, A. and L. Graciani (1996) Symbolic nonlinear analysis and control package, Proc. 13th IFAC World Congress, San Francisco, F, 295–298
Jiang, Z. P. and L. Praly (1991) Iterative designs of adaptive controllers for systems with nonlinear integrators, Proc. 30th IEEE Conference on Decision and Control, Brighton, UK, 2482–2487
Kanellakopoulos, I., P.V. Kokotović and A. S. Morse (1991) Systematic Design of Adaptive Controllers for Feedback Linearizable Systems, IEEE Trans. Automat. Contr., 36, 1241–1253
Koshkouei, A. J. and A.S.I. Zinober (1999) Adaptive Sliding Backstepping Control of Nonlinear Semi-Strict Feedback Form Systems, Proc. 7th IEEE Mediterranean Control Conference, Haifa
Koshkouei, A.J. and A.S.I. Zinober (2000) Adaptive Output Tracking Backstepping Sliding Mode Control of Nonlinear Systems, Proc. 3rd IFAC Symposium on Robust Control Design, Prague
Koshkouei, A.J. and A.S.I. Zinober (2000), Adaptive Backstepping Control of Nonlinear Systems with Unmatched Uncertainty, submitted to CDC2000, Sydney
Kravaris, C. and S. Palanki (1988) AIChE Journal, 34, 1119–1127
Krstić, M., I. Kanellakopoulos and P.V. Kokotović (1992) Adaptive Nonlinear Control without Overparametrization, Systems and Control Letters, 19, 177–185
Krstić, M., I. Kanellakopoulos, and P.V. Kokotović (1995) Nonlinear and Adaptive Control Design, New York: John Wiley & Sons
Marino, R. and P. Tomei (1995) Nonlinear Control Design, London: Prentice-Hall
Rios-Bolívar, M. (1997) Adaptive Backstepping and Sliding Mode Control of Uncertain Nonlinear Systems, PhD dissertation, Applied Mathematics, University of Sheffield
Rios-Bolívar, M., H. Sira-Ramírez and A. S. I. Zinober (1995) Output Tracking Control via Adaptive Input-Output Linearization: A Backstepping Approach, Proc. 34th IEEE CDC, New Orleans, 2, 1579–1584
Rios-Bolívar, M. and A.S.I. Zinober (1994) Sliding mode control for uncertain linearizable nonlinear systems: A backstepping approach, Proc. 3rd IEEE Workshop on Robust Control via Variable Structure and Lyapunov Techniques, Benevento, Italy, 78–85
Rios-Bolívar, M. and A.S.I. Zinober (1997a) Dynamical adaptive backstepping control design via symbolic computation, Proc. 3rd European Control Conference, Brussels
Rios-Bolívar, M. and A.S.I. Zinober (1997b) Dynamical adaptive sliding mode output tracking control of a class of nonlinear systems, Int. J. Robust and Nonlinear Control, 7, 387–405
Rios-Bolívar, M., and A.S.I. Zinober (1998) A symbolic computation toolbox for the design of dynamical adaptive nonlinear control, Appl. Math. and Comp. Sci., 8, 73–88
Rios-Bolívar, E.M. and Zinober, A.S.I. (1999) Dynamical adaptive sliding mode control of observable minimum-phase uncertain nonlinear systems, in “Variable structure systems, sliding mode and nonlinear control”, ed K.D. Young and Ü. Özgüner, Springer-Verlag, London, 211–235
Rios-Bolívar, M., A.S.I. Zinober and H. Sira-Ramírez (1996) Dynamical Sliding Mode Control via Adaptive Input-Output Linearization: A Backstepping Approach, in: Robust Control via Variable Structure and Lyapunov Techniques (F. Garofalo and L. Glielmo, Eds.), Springer-Verlag, 15–35
Rios-Bolívar M., A.S.I. Zinober and H. Sira-Ramírez (1997) Dynamical Adaptive Sliding Mode Output Tracking Control of a Class of Nonlinear Systems, Int. J. Robust and Nonlinear Control, 7, 387–405
Rothfuss, R. and M. Zeitz (1996) A toolbox for symbolic nonlinear feedback design”, Proc. 13th IFAC World Congress, San Francisco, F, 283–288
Sira-Ramírez, H. and M. Delgado Passivity Based Regulation of Nonlinear Continuous Processes (to be published in Advances in Control)
Sira-Ramírez, H. and O. Llanes-Santiago (1994) Dynamical Feedback Strategies in the Regulation of Nonlinear Chemical Processes, IEEE Trans. Control Systems Technology, 2, 11–21
Slotine, J-J. E. and W. Li (1991) Applied Nonlinear Control, Prentice-Hall, London
Sontag, E. D. (1989) Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Contr., 34, 435–443
Yao, B. and M. Tomizuka (1997) Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form, Automatica, 33, 893–900
Zinober, A.S.I., J.C. Scarratt, A. Ferrara, L. Giacomini and E.M. Rios-Bolívar (1999) Dynamical adaptive first and second order sliding mode control of nonlinear non-triangular uncertain systems, Proc. 7th IEEE Mediterranean Control Conference, Haifa
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2001 Springer-Verlag London Limited
About this paper
Cite this paper
Zinober, A.S.I., Scarratt, J.C., Mills, R.E., Koshkouei, A.J. (2001). New developments in dynamical adaptive backstepping control. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110326
Download citation
DOI: https://doi.org/10.1007/BFb0110326
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-85233-364-5
Online ISBN: 978-1-84628-569-1
eBook Packages: Springer Book Archive