Abstract
The chapter introduces a technique for multi-variable extremum seeking and gradient seeking, employing distinct noise sources for each of the distinct inputs being tuned. Convergence is proved using the averaging method, with an estimate of the convergence rate being related to the eigenvalues of the Hessian matrix of the map.
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References
Blankenship G, Papanicolaou GC (1978) Stability and control of stochastic systems with wide-band noise disturbances. I. SIAM J Appl Math 34:437–476
Freidlin MI, Wentzell AD (1984) Random perturbations of dynamical systems. Springer, Berlin
Khas’minskiı̌ RZ, Yin G (2004) On averaging principles: an asymptotic expansion approach. SIAM J Math Anal 35:1534–1560
Kushner HJ, Ramachandran KM (1988) Nearly optimal singular controls for wideband noise driven systems. SIAM J Control Optim 26:569–591
Liu S-J, Krstic M (2010) Continuous-time stochastic averaging on infinite interval for locally Lipschitz systems. SIAM J Control Optim 48:3589–3622
Skorokhod AV (1989) Asymptotic methods in the theory of stochastic differential equations. Translations of mathematical monographs. Amer Math Soc, Providence
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© 2012 Springer-Verlag London
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Liu, SJ., Krstic, M. (2012). Multi-parameter Stochastic Extremum Seeking and Slope Seeking. In: Stochastic Averaging and Stochastic Extremum Seeking. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4087-0_8
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DOI: https://doi.org/10.1007/978-1-4471-4087-0_8
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4086-3
Online ISBN: 978-1-4471-4087-0
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