Decision and Control Lecture Series
Decision and Control Laboratory, Coordinated Science Laboratory
Dyadic Perturbation Observer Framework for Control of a Class of Nonlinear PDE/ODE Systems
Postdoctoral Researcher, University of Illinois
Future Assistant Professor in Mechanical Engineering, McGill University
Wednesday, August 28, 2013
3:00 p.m. to 4:00 p.m.
The control of systems described by partial differential equations (PDEs) is a challenging problem. In particular, unlike systems described by ordinary differential equations (ODEs), methods for systems described by nonlinear PDEs are usually case-specific. In this talk, I will present an approach for controlling nonlinear systems, called a dyadic perturbation observer (DPO), which was developed primarily as a generic (as against a case-specific) method for the boundary control of systems described by PDEs. The method is equally applicable to a system of nonlinear ODEs. This approach decomposes the system into two parts: a linear (homogeneous) system with just the control signal but no nonlinearities, and a nonlinear (particular) system without the control input (and homogeneous boundary conditions for PDE systems). The control signal is designed to ensure that the output of the homogeneous system tracks the desired output minus the output of the ``particular'' system. The stability of the closed loop system is proved using the small gain theorem. The method is demonstrated through simulations as well as in experiments on a bending beam.
Aditya Paranjape was born in Mumbai, India. He received the degrees of B. Tech and M. Tech from IIT Bombay in 2007, and Ph.D. from UIUC in 2011, all of them in Aerospace Engineering. He is currently a postdoctoral researcher with Prof. Soon-Jo Chung, and will start shortly as a faculty member in Mechanical Engineering at McGill University, Montreal, Canada. His research interests include flight dynamics and nonlinear control.