Extremum seeking for optimal control problems with unknown time‐varying systems and unknown objective functions. (25th February 2020)

• Record Type: Journal Article
• Authors: Scheinker, Alexander; Scheinker, David
• Other Names: Benosman Mouhacine guestEditor.; Krstić Miroslav guestEditor.; Guay Martin guestEditor.; Teel Andrew guestEditor.
• Is Part Of: International journal of adaptive control and signal processing. Volume 35:Number 7(2021)
• Page Start: 1143
• Page End: 1161
• Publication Date: 2020-02-25
• Subjects: extremum seeking -- industrial applications of optimal control -- iterative schemes -- optimal control -- optimal controller synthesis for systems with uncertainties -- time‐varying systems; Adaptive control systems -- Periodicals; Adaptive signal processing -- Periodicals; 629.836
• DOI: 10.1002/acs.3097
• Languages: English
• ISSNs: 0890-6327

Abstract

Summary: We consider the problem of optimal feedback control of an unknown, noisy, time‐varying, dynamic system that is initialized repeatedly. Examples include a robotic manipulator which must perform the same motion, such as assisting a human, repeatedly and accelerating cavities in particle accelerators which are turned on for a fraction of a second with given initial conditions and vary slowly due to temperature fluctuations. We present an approach that applies to systems of practical interest. The method presented here is model independent; does not require knowledge of the objective function; is robust to measurement noise; is applicable for any set of initial conditions; is applicable to simultaneously controlling an arbitrary number of parameters; and may be implemented with a broad range of continuous or discontinuous functions such as sine or square waves. For systems with convex cost functions we prove that our algorithm will produce controllers that approach the minimal cost. For linear systems we reproduce the cost minimizing linear quadratic regulator optimal controller that could have been designed analytically had the system and cost function been known. We demonstrate the effectiveness of the algorithm with simulation studies of noisy and time‐varying systems.