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The Center for Control, Dynamical Systems, and Computation University of California at Santa Barbara

Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Spring 2010 Seminar Series
Control of Nonlinear System over Uncertain Channels:
Performance Limitations and Non-Equilibrium Dynamics
Umesh Vaidya
Iowa State University
Friday, April 23, 2010, 3:00 4:00pm WEBB 1100
In this talk, we present results for the stabilization and observation of nonlinear systems over analog erasure channels. The
stochastic nature of the problem requires us to consider notions of stability adapted from ergodic theory of random dynami-
cal system. In particular, we employ almost sure and second moment exponential stability as the stability and performance
metric, respectively, to study this problem. The main result shows that while there are no limitations for the almost sure sta-
bilization, fundamental limitation arise for the second moment stabilization of nonlinear system over erasure channels. The
limitation for second moment exponential stabilization is expressed in terms of probability of erasure and global instability,
as captured by the positive Lyapunov exponents, of the open loop uncontrolled system. The dependence on the Lyapunov
exponents highlight, for the first time, the important role played by the global non-equilibrium dynamics of the nonlinear sys-
tems in determining the performance limitation. These results generalize the existing results known in the context of linear
time invariant system, where the Lyapunov exponents emerge as the natural generalization of eigenvalues from linear sys-


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics