Abstract
This chapter presents a new method of analyzing the stability of a class of nonlinear systems by using the DSC design approach. It is shown that the closed-loop error dynamics can be described by linear error dynamics with bounded perturbation terms that are a function of the error. The desired eigenvalues of the linear part can be assigned by choosing the control gains and filter time constants. Furthermore, based on quadratic stability theory, feasibility of the fixed controller gains for quadratic stabilization and tracking can be tested by solving a convex optimization problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barmish, B.R.: Necessary and sufficient conditions for quadratic stability of an uncertain system. J. Optim. Theory Appl. 46(4), 399–408 (1985)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
Brockman, M., Corless, M.: Quadratic boundedness of nonlinear dynamical systems. In: Proceedings of 34th IEEE Conference on Decision and Control, New Orleans, LA, pp. 504–509 (1995)
Brockman, M., Corless, M.: Quadratic boundedness of nominally linear systems. Int. J. Control 71(6), 1105–1117 (1998)
Gerdes, J.C.: Decoupled design of robust controllers for nonlinear systems: As motivated by and applied to coordinated throttle and brake control for automated highways. Ph.D. thesis, U.C. Berkeley, March 1996
Gerdes, J.C., Hedrick, J.K.: “loop-at-a-time” design of dynamic surface controllers for nonlinear systems. J. Dyn. Syst. Meas. Control 124, 104–110 (2002)
Grant, M., Boyd, S.: CVX: Matlab software for disciplined convex programming, version 1.21. http://cvxr.com/cvx/ (2011)
Hedrick, J.K., Yip, P.P.: Multiple sliding surface control: theory and application. J. Dyn. Syst. Meas. Control 122, 586–593 (2000)
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, New York (2002)
Krstić, M., Kanellakopoulous, I., Kokotović, V.P.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)
Petersen, I.R.: Quadratic stabilizability of uncertain linear systems: existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control. IEEE Trans. Autom. Control 30(3), 291–293 (1985)
Sturm, J.F.: Using SeDuMi 1.02, a matlab toolbox for optimization over symmetric cones
Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)
The Mathworks: Symbolic math toolbox 5 user’s guide. Available in http://www.mathworks.com/products/symbolic/ (2010)
Toh, K., Tütüncü, R., Todd, M.: SDPT3 4.0 (beta) (software package) (2006)
Yip, P.P.: Robust and adaptive nonlinear control using dynamic surface controller with applications to intelligent vehicle highway systems. Ph.D. dissertation, University of California, Berkeley (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Song, B., Hedrick, J.K. (2011). Dynamic Surface Control. In: Dynamic Surface Control of Uncertain Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-632-0_2
Download citation
DOI: https://doi.org/10.1007/978-0-85729-632-0_2
Publisher Name: Springer, London
Print ISBN: 978-0-85729-631-3
Online ISBN: 978-0-85729-632-0
eBook Packages: EngineeringEngineering (R0)