Close-Loop Stochastic Dynamic Optimization Under Probabilistic Output-Constraints

Abstract

In this work, two methods based on a nonlinear MPC scheme are proposed to solve close-loop stochastic dynamic optimization problems assuring both robustness and feasibility with respect to output constraints. The main concept lies in the consideration of unknown and unexpected disturbances in advance. The first one is a novel deterministic approach based on the wait-and-see strategy. The key idea is here to anticipate violation of output hard-constraints, which are strongly affected by instantaneous disturbances, by backing off of their bounds along the moving horizon. The second method is a new stochastic approach to solving nonlinear chance-constrained dynamic optimization problems under uncertainties. The key aspect is the explicit consideration of the stochastic properties of both exogenous and endogenous uncertainties in the problem formulation (here-and-now strategy). The approach considers a nonlinear relation between the uncertain input and the constrained output variables.