Boundary Control of Burgers' Equation by Input-Output Linearization

This paper addresses the boundary control law of a viscous Burgers' equation with a Dirichlet actuation. The control objective consists in achieving a desired set point for a punctual output defined at a given spatial position. This control problem is characterized by an infinite characteristic index. To tackle this problem in the framework of geometric control, a design approach based on the concept of the characteristic index is proposed. First, it is proposed to convert the boundary control problem to an equivalent punctual control problem based both on the linearization of the equation and the Laplace transform in space domain. Then, to have a finite characteristic index, an auxiliary controlled output is defined and a control law that achieves a global linearization between an external variable (desired set point) and this auxiliary output is derived. To enforce set point tracking of the original punctual output, a control strategy is proposed based on the steady state relation between the punctual and the auxiliary outputs. The performance of the proposed control strategy is evaluated via numerical simulation runs.