Numerical solutions to the optimal stabilization Hamilton-Jacobi PDE in control theory

PLEASE NOTE: This is a WEBINAR

A problem of practical interest in control theory is to stabilize a nonlinear dynamical system through the action of a feedback control.  The stabilization problem can be embedded as an optimal control problem leading one to solve a Hamilton-Jacobi (HJ) PDE.  The associated HJ equation is a first order nonlinear singular PDE and, under suitable conditions, can be solved locally using power series methods.  In this talk, I will present a numerical method that extends the domain of validity of the power series approach.  The method relies on patchy vector field techniques, level set methods, and a Cauchy-Kowalevski continuation algorithm.  The method will be illustrated on 2D-3D control systems.