Advantages of using relevant nearly optimal solutions in multi-objective tuning of robust controllers

This paper presents a new approach for the multiobjective optimal design of robust controllers in systems with stochastic parametric uncertainty. Traditionally, uncertainty is incorporated into the optimization process. However, this can generate two problems: (1) low performance in the nominal scenario; and (2) high computational cost. For the first point, it is possible to ensure that the controllers produce an acceptable performance for the nominal scenario in exchange for being lightly robust. For the second point, the methodology proposed in this work reduces the computational cost significantly. This approach addresses uncertainty by analyzing the robustness of optimal and nearly optimal controllers in the nominal scenario. The methodology guarantees obtaining controllers that are similar/neighboring to lightly robust controllers. Two examples of controller design are shown: one for a linear model and another for a nonlinear model. Both examples demonstrate the usefulness of the proposed new approach.