Feedback Stabilization of Incompressible Flows using the Quadratic Constraint Framework

Flow instabilities can create high shear regions that are detrimental to the performance of engineering systems. In this talk, we propose a framework to synthesize globally stabilizing feedback controllers to suppress such instabilities. The framework exploits the fact that the nonlinearity in the incompressible Navier-Stokes equations (NSE) is energy conserving. This property is expressed as a quadratic constraint and juxtaposed with the linear dynamics of NSE for controller synthesis using semi-definite programming (SDP). The resulting framework can be used to design full-state and static-output feedback controllers that stabilize the flow regardless of the perturbation magnitude.  We demonstrate the approach on a reduced-order model of plane Couette flow with body force actuation.