ICMA 2012 Conference
Source Seeking for Nonholonomic Vehicles Using Deterministic and Stochastic Averaging
Miroslav Krstic, Ph.D.
Professor and Director
Cymer Center for Control Systems and Dynamics
University of California, San Diego
La Jolla, CA 92093-0411, U.S.A.
Source seeking is the problem of stabilization of an unknown system by feedback of output only, where the output map is known to be convex (or concave) but is otherwise unknown. Such a problem arises in applications of mobile robots to localizing sources of chemical or other signals in environments where position is not measurable (such as under water or indoors). We present algorithms that guide a robot up the gradient of an unknown field, with the help of perturbation signals. Two classes of signals are considered: deterministic periodic perturbations and stochastic perturbations. For deterministic perturbations, we employ the classical averaging theory to prove stability of the search algorithms and estimate their convergence rates. For stochastic perturbations, with Professor Shujun Liu of Southeast University we develop new theorems of stochastic averaging, with which we prove stability in probability and quantify the convergence rates. Not only one, but an arbitrary number of robots can be guided to the source using a single control law that is simultaneously applied to all the robots.
Biography for Dr. Miroslav Krstic
Miroslav Krstic is the Daniel L. Alspach Professor of Dynamic Systems and Control at University of California, San Diego, and the founding director of the Cymer Center for Control Systems and Dynamics at UCSD. He is a co-author of eight books, including the classic Nonlinear and Adaptive Control Design (1995), one of the two most cited research monographs in control theory, the recent single-authored Delay Compensation for Nonlinear, Adaptive, and PDE Systems (466 pages, Birkhauser, October 2009), and other books on control of turbulent fluid flows, stochastic nonlinear systems, and extremum seeking. Krstic has held the Russell Severance Springer Distinguished Visiting Professorship at UC Berkeley and the Harold W. Sorenson Distinguished Professorship at UC San Diego. He is a recipient of the PECASE, NSF Career, and ONR Young Investigator Awards, as well as the Axelby and Schuck Paper Prizes. Krstic was the first recipient of the UCSD Research Award in the area of engineering. He is a Fellow of IEEE and IFAC and serves as Senior Editor in IEEE Transactions on Automatic Control and Automatica.