Control of burgers’ system via parametrization 1

Abstract Control of nonlinear partial differential equation (PDE) models including the boundary conditions are studied. Construction of open-loop control and the corresponding output is based on the parametrization concept. It is, in principle, extension of the flatness issue of ordinary differential equation systems to PDEs. Here as a test example of nonlinear PDE systems is the viscous Burgers’ equation with boundary control. The control objective is to drive the system from one stable steady-state to another in a finite time. Burgers’ system is converted via Hopf-Cole transformation to the linear heat equation. Then parametrization via pseudo-differential-algebraic methods of the linear heat system is carried out. Via the inverse transformation parametrization of the original nonlinear Burgers’ system is obtained. Some outlines how to apply these specific results to other nonlinear PDE systems are given, too. Numerical studies of finite-time control results for a parametrization function complete the paper.