Worst-case analysis of distributed parameter systems with application to the 2D reaction–diffusion equation‡

It is well known that optimal control trajectories can be highly sensitive to perturbations in the model parameters. Computationally efficient numerical algorithms are presented for the worst-case analysis of the effects of parametric uncertainties on boundary control problems for finite-time distributed parameter systems. The approach is based on replacing the full-order model of the system with a power series expansion that is analyzed by linear matrix inequalities or power iteration, which are polynomial-time algorithms. Theory and algorithms are provided for computing the most positive and most negative worst-case deviation in a state or output, in contrast to the ‘two-sided’ deviations normally computed in worst-case analyses. Application to the Dirichlet boundary control of the reaction–diffusion equation to track a desired two-dimensional concentration field illustrates the promise of the approach. Copyright q 2010 John Wiley & Sons, Ltd.