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Global optimality in model predictive control via hidden invariant convexity

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Document pages: 12 pages

Abstract: Non-convex optimal control problems occurring in, e.g., water or powersystems, typically involve a large number of variables related throughnonlinear equality constraints. The ideal goal is to find a globally optimalsolution, and numerical experience indicates that algorithms aiming forKarush-Kuhn-Tucker points often find (near-)optimal solutions. In our paper, weprovide a theoretical underpinning for this phenomenon, showing that on a broadclass of problems the objective can be shown to be an invariantly convexfunction (invex function) of the control decision variables when statevariables are eliminated using implicit function theory. In this way,near-global optimality can be demonstrated, where the exact nature of theglobal optimality guarantee depends on the position of the solution within thefeasible set. In a numerical example, we show how high-quality solutions areobtained with local search for a river control problem where invexity holds.

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