Coordinated Science Laboratory
“Analytic Left Inversion for Multivariable Input-Output Systems”
Luis A. Duffaut Espinosa, Ph.D.
University of Vermont
Wednesday, March 8, 2017
3:00 p.m. to 4:00 p.m.
CSL Auditorium (B02)
Given a multi-input, multi-output (MIMO) system, F, and a function y in the range of F, the left inversion problem is to determine an input u such that y=F[u]. This talk describes a framework under which an exact and explicit analytical solution to this problem is obtained when F is an analytic mapping in the sense that it has a convergent Chen-Fliess functional expansion, and y is a real analytic function. In particular, given a certain condition on the generating series c of F is satisfied, a unique analytic u can always be determined via operations on formal power series. The condition on c turns out to be equivalent to having a well-defined relative degree when F has an input-affine analytic state space realization with finite dimension. But the method is applicable even when F does not have such a realization. The technique is demonstrated on two examples: motion planning for a bi-steerable car and trajectory control for a Lotka-Volterra system.
Luis A. Duffaut Espinosa received his Ph.D. in electrical and computer engineering from the Old Dominion University in 2009. He is currently on the faculty of the Electrical and Biomedical Engineering Department of the University of Vermont in Burlington, Vermont. His research interests include modeling and control theory for nonlinear systems, power systems, algebraic combinatorics, quantum control and complex systems.