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Partial outer convexification is a relaxation technique for MIOCPs being constrained by time-dependent differential equations. Sum-Up-Rounding algorithms allow to approximate feasible points of the relaxed, convexified continuous problem with binary ones that are feasible up to an arbitrarily small δ > 0. We show that this approximation property holds for ODEs and semilinear PDEs under mild regularity assumptions on the nonlinearity and the solution trajectory of the PDE. In particular, requirements of differentiability and uniformly bounded derivatives on the involved functions from previous work are not necessary to show convergence of the method.Mathematics Subject Classification. 49M20, 49N60, 90C11, 49J20.

Designing an exoskeleton to reduce the risk of lowback injury during lifting is challenging. Computational models of the human-robot system coupled with predictive movement simulations can help to simplify this design process. Here, we present a study that models the interaction between a human model actuated by muscles and a lower-back exoskeleton. We provide a computational framework for identifying the spring parameters of the exoskeleton using an optimal control approach and forward-dynamics simulations. This is applied to generate dynamically consistent bending and lifting movements in the sagittal plane. Our computations are able to predict motions and forces of the human and exoskeleton that are within the torque limits of a subject. The identified exoskeleton could also yield a considerable reduction of the peak lower-back torques as well as the cumulative lower-back load during the movements. This work is relevant to the research communities working on human-robot interaction, and can be used as a basis for a better human-centered design process.