Providing certificates of global optimality or robustness in dynamic optimization problems remains a formidable challenge. The development of reliable methods to tackle these problems, such as complete‐search algorithms, and the analysis of these methods constitutes an exciting research topic. A particular focus over the past few decades has been on computing both tight approximations and rigorous enclosures for the reachable set of parametric/uncertain dynamic systems, with developments scattered across the control, optimization, and reliable computing literature. Despite significant advances, only simple dynamic systems either comprising a small number of states or subject to a small level of uncertainty can be tackled with these methods to this day. Attempts have also been made to embed these methods within global and robust dynamic optimization solvers, but these approaches are themselves restricted to simple, small‐scale problems only. In this special issue of Optimal Control Applications and Methods, we are providing a selection of articles that feature novel algorithmic developments to address some of these outstanding challenges.The paper by Harwood and Barton presents a novel approach to computing affine relaxations on the solutions of constrained parametric ordinary differential equations (ODEs). They developed an extension of differential inequality–based comparison theorems, whereby a polyhedral outer
Optimal Control Applications and Methods – Wiley
Published: Jan 1, 2018
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