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Path-following: an Alternative to Reference Tracking

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Abstract:
The main objective in path-following is to steer a physical object to converge to and move along a geometric path. A secondary objective is to ensure that object's motion along the path satisfies a given dynamic specification. Path-following is a relaxation of standard reference tracking motivated by applications in which temporal errors are more acceptable than spatial errors, such as control of robots, vehicles, aircrafts, CNC machines, etc. In a path-following problem the time dependence of the motion is suppressed by parameterizing the path with an auxiliary variable $\theta$. The problem is first solved with respect to $\theta$, leaving the choice of a timing law for $\theta$ as a function of time and system's state as an additional degree of freedom. We provide constructive procedures for exploiting the freedom to design the timing law, that is, the freedom obtained by recasting a reference tracking problem into the path-following framework. In the first part of the talk we design the timing law to reduce the control effort. While maintaining the desired convergence to the path, our design provides a tradeoff between the dynamic performance along the path and the control effort. In the second part of this talk we develop several designs, depending on a system at hand, in which the timing law is constructed to stabilize the unstable zero dynamics. These path-following designs avoid the obstacle on tracking accuracy imposed by the unstable zero dynamics in a variety of practically relevant situations. The benefits of the developed path-following designs are illustrated on several practical examples.

Type of Seminar:
Symposium on Control and Computation
Speaker:
Dr. Dragan Dacic
University of California, Santa Barbara, USA
Date/Time:
Jun 28, 2005   9:15
Location:

ETH-Zentrum, Gloriastrasse 35, Zurich, Building ETZ, Room E6
Contact Person:

Prof. M.Morari
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Biographical Sketch:
Dragan Dacic got his B.Sc. degree in Electrical Engineering from University of Belgrade in 1999, and his M.Sc. and Ph.D. degree in Electrical Engineering from University of California, Santa Barbara, in 2001 and 2005, respectively. His research interests include nonlinear control design, path-following and reference tracking, fundamental limitations in control systems, sampled-data control of nonlinear systems, and applications in biomedical systems. He is currently working on path-following for infinite-dimensional systems on lattices with his collaborators at University of Minnesota, Minneapolis, and on utilization of state-dependent sampling for control of nonlinear systems with collaborators at University of Melbourne.