Clipping-off gradient algorithms to compute optimal controls with constrained magnitude

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Abstract
This paper presents a clipping-off technique which, when used in association with gradient methods in function space, can be used to solve non-linear optima control problems with magnitude constraint on the control inputs. The proposed clipping-off gradient algorithms are simple to implement on a digital computer and preserve the large range of convergence of first-variational methods. Several numerical examples are included, one of which contains two state-variable inequality constraints and a magnitude constraint on the control input