Modeling and Control of Partial Differential Equations (PDE) Described Systems

This proposed research is aimed to develop a novel modeling and control algorithm for the PDE described systems. When dealing with time-dependent PDE problems, the partial derivatives of a function over spatial variables are obtained by approximating the function values at interpolation nodes and their corresponding neighbors as a finite summation of polynomial series. A cluster of interpolation nodes guarantees the boundedness of the residual derivatives. Substituting these approximations in the PDE and discretizing the spatial domain of variables while keeping the time domain continuous yields a system of ODEs. By using an eigenvalue-based technique, a reduced-order model is derived, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE is augmented with nonlinear time-varying uncertainties and unmodeled dynamics. The final goal is to design an L1 adaptive controller for handling of model mismatch and delivering a good tracking performance.