Towards Redundant Constraint Removal in Scenario Approximation of Optimal Control Problems with Multiplicative Model Uncertainty

Abstract

Randomised approaches, such as the scenario approach, are employed to approximately solve robust optimisation problems with possibly infinite number of convex constraints. The idea is to solve the optimisation problem with a finite number of constraints randomly drawn from the original set of constraints. Precise results bounding how many constraints need to be drawn in order for the approximate problem solution to be a feasible solution for the original problem, with a given probability, are provided by the scenario theory. However, the number of constraints in the scenario problem can be large when there are many optimisation variables and the required probability of feasibility for the original problem is high, which can lead to intractable computational burden. This paper exploits the structure of linear constraints with additive and multiplicative uncertainties, and proposes an algorithm for removing redundant constraints, prior to solving the optimisation problem. The computational complexity of the algorithm is linear in the number of constraints, and the algorithm is illustrated in a simulation example and the computational savings are evaluated.