Extremum seeking under stochastic noise and applications to mobile sensors

• Published in: Automatica (Oxford) Vol. 46; no. 8; pp. 1243 - 1251
• Main Authors: STANKOVIC, Miloš S, STIPANOVIC, Dušan M
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2010; Elsevier
• Subjects: Algorithms; Applied sciences; Automatic control; Computer science; control theory; systems; Control theory. Systems; Convergence; Exact sciences and technology; Extremum seeking; Gain; Information technology; Informationsteknik; Mobile sensors; Noise; Noise source localization; Optimization; Perturbation; Reglerteknik; Sensors; Stochastic recursive algorithms; Stochasticity; TECHNOLOGY; TEKNIKVETENSKAP; Extremum seeking; Stochastic recursive algorithms; Noise source localization; Mobile sensors; Convergence; Extreme search; Probabilistic approach; Measurement sensor; Recursive algorithm; Time varying system; Noise source; Source localization; Signal to noise ratio
• ISSN: 0005-1098; 1873-2836; 1873-2836
• DOI: 10.1016/j.automatica.2010.05.005

In this paper the extremum seeking algorithm with sinusoidal perturbations has been extended and modified in two ways: (a) the output of the system is corrupted with measurement noise; (b) the amplitudes of the perturbation signals, as well as the gain of the integrator block, are time varying and tend to zero at a pre-specified rate. Convergence to the extremal point, with probability one, has been proved. Also, as a consequence of being able to cope with a stochastic environment, it has been shown how the proposed algorithm can be applied to mobile sensors as a tool for achieving the optimal observation positions. The proposed algorithm has been illustrated through several simulations.