• Dr. Umesh Vaidya
  • Iowa State University
  • 113 McBryde Hall
  • 4:00 p.m.
  • Faculty Host: Dr. Cornel Sultan

Analysis and control of uncertain nonlinear systems exhibiting non-equilibrium dynamics is of interest in various applications such as fluid flow control, electric power grid, and biological systems. In this talk we present results on the novel ergodic theory-based framework for the analysis and control of non-equilibrium dynamics in uncertain dynamical systems. Our first main result is on the introduction of Lyapunov measure as a new tool for stability verification and stabilization of non-equilibrium dynamics in nonlinear systems. The main contribution of this work is that it provides for a systematic linear programming based solution for the stability verification and stabilization of nonequilibrium dynamics in nonlinear systems. The novel framework is also used to study the problems of stabilization and estimation of nonlinear systems over uncertain channels and interconnections. The main results prove that fundamental limitations arise in the stabilization and estimation of nonlinear systems over uncertain channels, expressed in terms of channel uncertainty and positive Lyapunov exponents of the open loop nonlinear system. The positive Lyapunov exponents capture the global instability of nonlinear systems. Hence our results highlights, for the first time, the important role-played by the global nonequilibrium dynamics in obtaining the limitation results. The framework is extendable to study more general control problems over uncertain networks with nonlinear components dynamics.