155. NONLINEAR DYNAMICS AND CONTROL

Department: Mechanical & Aerospace Engineering
Research Institute Affiliation: Center for Control Systems and Dynamics (CCSD)
Faculty Advisor(s): Miroslav Krstic

Primary Student
Name: Alex Scheinker
Email: ascheink@ucsd.edu
Phone: 858-822-1936
Grad Year: 2013

Abstract
The control of complex systems is difficult due to the interaction of many control parameters coupled with limited numbers of sensors. These difficulties are further compounded by a lack of accurate real-time modeling. Given a complicated system's output or any other performance measurements, a typical control system has only a very basic model, usually linearized around specific operating points. The main advantage of simplified models is that they are very fast and can quickly simulate system performance and give outputs that may guide operators. Ignoring the detailed nonlinear terms may be acceptable for very small and stable systems; however, for large nonlinear and unstable systems small perturbations quickly build up through complex interactions with other components and can have significant negative effects. Applying a perturbation-driven extremum seeking algorithm to time-varying systems whose parameters are unknown and satisfy certain bounds is an attempt to deal with the nonlinear system in its entirety. The results demonstrate a class of systems for which extremum-seeking controllers, unaware of the system's detailed dynamics, exist and are capable of driving the systems to an equilibrium or to track a given trajectory over a wide range of starting conditions, not limited to local linearized results. Theoretically this work is applicable to any observable system which can tolerate a high frequency oscillatory control input.

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