Professor Jeff Borggaard
Department of Mathematics (office: McB 528)
Interdisciplinary Center for Applied Mathematics
The talk will begin by providing linear feedback control solutions to flow control problems governed by the Navier-Stokes equations. This involves model reduction and control design for the linearized system. While there are successful cases, this example also motivates the need for more sophisticated feedback laws that fully incorporate the nonlinear term. We then present an algorithm for computing nonlinear feedback control laws for autonomous quadratic systems of equations that lead to an easily computed series solution for the feedback law. This algorithm is based on that provided by Al'brekht in 1961, and extended by Krener et al., but the specialization to systems with quadratic nonlinearities and quadratic control costs makes it feasible to compute terms of the feedback law out to 5th degree terms for modest sized problems. The speed of the algorithm leverages a newly released tensor-based recursive algorithm for linear systems by Chen and Kressner. We will provide some examples that are generated by discretizing the one-dimensional Burgers equation (a simple model that is often used as a substitute for the Navier-Stokes equations when developing new control algorithms).