Trajectory Planning for Boundary Controlled Parabolic PDEs With Varying Parameters on Higher-Dimensional Spatial Domains

The flatness-based design of a feedforward tracking control is considered for the solution of the trajectory planning problem for a boundary controlled diffusion-convection-reaction system with spatially and temporally varying parameters defined on a 1 les m-dimensional parallelepipedon with the nonlinear input being restricted to a (m-1) -dimensional hyperplane. For this, an implicit state and input parametrization in terms of a basic output is determined via a Volterra-type integral equation with operator kernel. By recursively computing successive series coefficients, a series solution of the integral equation is obtained, whose absolute and uniform convergence is verified by restricting the system parameters and the basic output to a certain but broad Gevrey class. Hence, prescribing an admissible desired trajectory for the basic output directly yields the feedforward control by evaluating the input parametrization. This results in a systematic procedure for trajectory planning and feedforward control design for boundary controlled parabolic distributed-parameter systems defined on higher-dimensional domains.