Randomization methods in optimization and adaptive control - Dedicated to Tyrone Duncan on occasion of his 60th birthday

• We consider simultaneous perturbation stochastic approximation (SPSA) methods applied to noise-free problems in optimization and adaptive control. More generally, we consider discrete-time fixed gain stochastic approximation processes that are defined in terms of a random field that is identically zero at some point theta*. The boundedness of the estimator process is enforced by a resetting mechanism. Under appropriate technical conditions the estimator sequence converges to theta* with geometric rate almost surely. This result is in striking contrast to classical stochastic approximation theory where the typical convergence rate is n(-1/2). For the proof a discrete-time version of the ODE-method is used and the techniques of [10] are extended. A simple variant of noise free-SPSA is applied to extend a direct controller tuning method named Iterative Feedback Timing (IFT), see [16]. Using randomization, the number of experiments required to obtain an unbiased estimate of the gradient of the cost function can be reduced significantly for multi-input multi-output systems.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

PERTURBATION GRADIENT APPROXIMATION

STOCHASTIC-APPROXIMATION

CONVERGENCE

ALGORITHM

SRA - ICT

SRA - Informations- och kommunikationsteknik

Publication and Content Type

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