Control of spatially distributed processes with unknown transport-reaction parameters via two layer system adaptations

The control problem of dissipative distributed parameter systems described by semilinear parabolic partial differential equations with unknown parameters and its application to transport-reaction chemical processes is considered. The infinite dimensional modal representation of such systems can be partitioned into finite dimensional slow and infinite dimensional fast and stable subsystems. A combination of a model order reduction approach and a Lyapunov-based adaptive control technique is used to address the control issues in the presence of unknown parameters of the system. Galerkin's method is used to reduce the infinite dimensional description of the system; we apply adaptive proper orthogonal decomposition (APOD) to initiate and recursively revise the set of empirical basis functions needed in Galerkin's method to construct switching reduced order models. The effectiveness of the proposed APOD-based adaptive control approach is successfully illustrated on temperature regulation in a catalytic chemical reactor in the presence of unknown transport and reaction parameters.