The Department of Mathematics, Computer Science, and Statistics will host its monthly department seminar this Friday, April 19, at 3 p.m. in Fitzelle Hall, room 205. Dr. Laura Munteanu will present a talk entitled “Geometric Perspectives to Control Theory”.
Abstract: Control systems can be viewed as ordinary differential equations or dynamical systems involving a parameter. This parameter, called control, can be varied as to induce diverse trajectories of the given system through its solutions. More precisely, from a fixed point or state, we could reach an entire set of other states by varying the control. These are the so-called reachable sets, and the environment or the space in which the trajectories of certain control systems evolve may not necessarily be an Euclidean space but rather a differentiable manifold. These ideas led to the development of a new branch of control theory, called geometric control theory. In this presentation, we will discuss a few examples of both linear and nonlinear control systems, and we will look at how nonlinear control systems can be viewed as collections of vector fields on finite dimensional differentiable manifolds.