Robust Constraint Satisfaction for C/GMRES based on NMPC with Parameter Uncertainties

Abstract

Using optimization for solving control problems has become much more accessible due to computational advancements in recent years. With the introduction of Model Predictive Control (MPC) in the petro-chemical industry for linear plant models, nonlinear applications followed and enabled finding optimal control solutions for complex tasks. These tasks often require the abidance by certain limitations, which are referred to as constraints in a Nonlinear Model Predictive Control (NMPC) environment. This development entailed two major hurdles to be negotiated. The first one is finding efficient algorithms for problems such as NMPC optimizations, where Ohtsukas Continuation/Generalised Minimum Residual (C/GMRES) provides a remedy and is heavily used in this work. Second, improving model accuracy is an ongoing topic, which tries to eliminate model-plant mismatches, but usually fails to do so, because models solely approximate real plants. Hence, robust control approaches were introduced in order to deal with disturbances and inaccuracies. In this work, ideas from robust control are used and developed in order to deal with the problem of robustly satisfying inequality constraints on models with parameter uncertainties. Three approaches are presented, where the main goal is to find a worst case from a given parameter set. One method makes use of the fact that quasi-convex functions find their maximum at an extreme point of the functions argument and therefore enables finding the worst case via extreme point scenarios. Next, a method to find the worst case directly from the continuous parameter set is discussed, which is treated as a separate maximization problem, resulting in a bilevel optimization problem. A way of transforming such problems into singlelevel tasks via Karush- Kuhn-Tucker (KKT) conditions is presented, requiring the constraint function to be pseudo-concave. At last, sensitivity is discussed and used as a separate tool and to facilitate previous approaches.submitted by Markus KrierUniversität Linz, Masterarbeit, 2018(VLID)267997