Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems

A novel approach is proposed that quantifies the influence of parameter and control implementation uncertainties upon the states and outputs of finite-time control trajectories for nonlinear lumped and distributed parameter systems. The worst-case values of the states and outputs due to model parameter uncertainties are computed as a function of time along the control trajectories. The algorithm can also compute the part of the optimal control trajectory for which implementation inaccuracies are of increased importance. An analytical expression is derived that provides an estimate of the distribution of the states and outputs as a function of time, based on simulation results. The approaches require a relatively low computational burden to perform the analysis, compared to Monte Carlo approaches for robustness analysis. The technique is applied to the crystallization of an inorganic chemical with uncertainties in the nucleation and growth parameters and in the implementation of the control trajectory.