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Center for Nonlinear Studies |
In this talk, we explore the possibilities and limits of using computation to analyze and control complex distributed systems such as those which govern the magneto-hydrodynamics of a Tokamak. We begin the talk by showing how convex optimization and Sum-of-Squares can be used to optimize over the cone of positive polynomials. This result allows us to use positive matrices to parameterize positive Lyapunov functions for nonlinear differential equations. We then extend these results by showing how positive matrices can be used to parameterize the measures of energy which arise in infinite-dimensional systems such as those governed by delay-differential equations or PDEs. We then study the implications of this result for stability and control of systems with delay. Next, we discuss the problem of MHD stability in plasma and present several PDE models. We then show how we can use our results to analyze and design real-time controllers for these models which use only point observations and sources of non-inductive current.
Host: Marian Anghel