Decreasing the sensitivity of open-loop optimal solutions in decision making under uncertainty

We consider a framework for approximating the effects of uncertainty within the mean–variance optimization model for nonlinear systems. We present formulations for controlling the effects of parameter uncertainty characterized by continuous probability density functions. Robust strategies, capable of capturing up to second-order effects of the uncertainty, are derived and tested on a dynamic optimisation problem arising from a chemical engineering application. An associated sensitivity–robustness concept is discussed and shown to be an instance of the general approximation framework developed. The accuracy of the approximations (or the local nature of the robust solutions) is studied using Monte-Carlo simulations.