Abstract
Extremum seeking is realized via a state regulator that drives the state along a convergent set point sequence generated by a numerical optimization algorithm. In this chapter, we propose an asymptotic state regulator design for state feedback linearizable systems, where we trade off finite time state regulation to obtain flexibility in designing a robust extremum seeking controller. Existing techniques such as nonlinear damping and nonlinear adaptive control are then used to deal with input disturbance and unmodeled plant dynamics. Simulation examples illustrate the effectiveness of the basic and robust extremum seeking schemes, and design guidelines are provided for engineering applications. We also show that the NOESC scheme allows a large design flexibility for general nonlinear systems and performance functions, where the key is having the ability to design a robust regulator.
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
Notes
- 1.
Restrictions on D will result in the need for constrained optimization. The stability of constrained ESC is still an open topic of research.
References
Ariyur, K.B., Krstić, M.: Real-time Optimization by Extremum-seeking Control. Wiley-Interscience, Hoboken (2003)
Khalil, H.K.: Nonlinear Systems. Prentice Hall, Upper Saddle River (2001)
Mayhew, C.G., Sanfelice, R.G., Teel, A.R.: Robust source-seeking hybrid controllers for autonomous vehicles. In: Proceedings of the American Control Conference, pp. 1185–1190 (2007)
Moore, K.L.: Iterative learning control: An expository overview. In: Applied and Computational Controls, Signal Processing, and Circuits, vol. 1(1), pp. 425–488 (1998)
Nocedal, J., Wright, S.: Numerical Optimization. Springer, Berlin (1999)
Spooner, J.T., Maggiore, M., Ordóñez, R., Passino, K.M.: Stable Adaptive Control and Estimation for Nonlinear Systems, Neural and Fuzzy Approximator Techniques. Wiley, New York (2002)
Teel, A.R., Popović, D.: Solving smooth and nonsmooth multivariable extremum seeking problems by the methods of nonlinear programming. In: Proceedings of the American Control Conference, vol. 3, pp. 2394–2399 (2001)
Zhang, C., Ordóñez, R.: Non-gradient extremum seeking control of feedback linearizable systems with application to ABS design. In: Proceedings of the Conference Decision and Control, pp. 6666–6671 (2006)
Zhang, C., Ordóñez, R.: Robust and adaptive design of numerical optimization-based extremum seeking control. Automatica 45, 634–646 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag London Limited
About this chapter
Cite this chapter
Zhang, C., Ordóñez, R. (2012). Asymptotic State Regulator Design. In: Extremum-Seeking Control and Applications. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2224-1_5
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2224-1_5
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2223-4
Online ISBN: 978-1-4471-2224-1
eBook Packages: EngineeringEngineering (R0)