Generalized Tolerance Optimization for Robust System Design by Adaptive Learning of Gaussian Processes

A novel formulation of robust optimization is presented which is more general than existing ones. The solution of the associated optimization problem provides the largest tolerance set within the feasible design space which is defined by black-box performance measures. A learning-based optimization algorithm is introduced in which the feasibility of the tolerance set is evaluated based on Gaussian process models of the performance measures. The Gaussian process models are adaptively learned during the optimization, where new samples of promising tolerance sets are acquired by solving a constrained optimization problem by utilizing methods from semi-infinite programming. The usefulness of the proposed method is demonstrated by numerical studies. First, the achievable accuracy is investigated for a non-convex test function the analytical solution of which is known. Second, the methods are applied to challenging engineering problems, namely the automatic tuning of nonlinear model-predictive controllers, where the control plant is subject to parametric uncertainties. Here it is shown that the proposed methods can greatly outperform a tuning by human experts.