ICME Seminar: Sanjay Lall

Sanjay Lall of the Department of Aeronautics and Astronautics at Stanford University

Computation of Dynamic Invariants via Algebraic Set Representations

Recent developments in semidefinite programming and computational algebraic geometry have led to new algorithms for a wide class of non-convex and nonlinear optimization problems. This has led to new methods of computation for control systems.

In this talk we present a new approach for robustness analysis of nonlinear control systems. As an example, we focus on the problem of computing the region of attraction of an equilibrium point. For many nonlinear systems this region is difficult both to find and to represent efficiently. Instead of using a mesh discretization to

represent the sets, we represent the set algebraically, and use semidefinite programming to compute the coefficients in the representation. We further address the related problems of constraining the degree of the representations and the connectedness of the associated sets. We discuss some example applications including

deployment of flexible structures for spacecraft, as well as control systems.