Nonlinear Control of Diffusion Processes with Uncertain Parameters Using MRAC Approach

In this work a nonlinear controller for controlling diffusion processes with uncertain parameters is derived by using model reference adaptive control (MRAC) approach. The diffusion processes are described by linear, two-dimensional, parabolic partial differential equations. It is assumed that the uncertain parameters which appear only in the system equation are either constant or spatially-varying, and that distributed sensing and actuation are available. The nonlinear control laws are obtained by the Lyapunov redesign method. The exponential stability of the closed loop system is shown by applying averaging theorems.