Sliding Mode Observer for Fluid Flow

Many phenomena in science and engineering are described using partial differential equations. However, for the systems modeled by PDEs, having access to the states of the system can be challenging due to technical difficulties such as lacking enough sensors in the system. In this paper the problem of estimating the parameters of fluid flow described by distributed parameter systems is considered. Two simplified versions of Navier-Stokes equations, Burgers' and advection equations, are practiced to model the fluid dynamics. Using the principles of sliding mode control theory, the distributed parameter observer is designed in order estimate the parameters of the system having only limited number of measurements available.