141. OBSERVER DESIGN FOR AN IPDE WITH TIME-VARYING COEFFICIENTS
Name: Shuxia Tang
Grad Year: 2016
Inspired by a state-of-charge estimation problem for lithium-ion batteries, in which the system coefficients are time-varying, we consider a reaction-diffusion-advection integro-partial differential equation (IPDE) with (space-varying and) time-varying, possibly unbounded, coefficients (which have possibly unbounded derivatives) posed on (a finite space interval and) an infinite time interval. The problem is to design an observer for this system. To the best of our knowledge, there are no existing results of observer design for this class of IPDEs. Indeed, most of the existing references for stabilization or observer design problem of a PDE with time-varying coefficients consider a finite time interval, or the coefficients (and their derivatives) are required to be bounded with respect to the time variable. We employ the method of PDE backstepping, for which we would like to find a continuous transformation between the observer error system and an (exponentially) stable target system. Since the backstepping transform gain kernel satisfies an IPDE in which the coefficients are also time-varying, this makes the derivation of the existence and regularity of the kernel nontrivial. In order to deal with this difficulty, a majorant argument is utilized. Then, our designed observer is proved to be exponentially convergent. We believe that this result could serve as a starting point for stabilizing the class of IPDEs with time-varying, possibly unbounded, coefficients.
Industry Application Area(s)
Control Systems | Energy/Clean technology