Abstract
AbstractWe consider optimal switching of hybrid abstract evolution equations. The framework includes switching semilinear partial differential equations of parabolic or hyperbolic type, discontinuous state resets, switching costs and allows switching of the principle parts of the equations. We present adjoint‐based formulae for the gradient of the cost functional with respect to position and number of switching time points that lead to first order necessary conditions. Moreover, we discuss an alternate‐direction approach for implementing descent methods. As an application we consider optimal open/close‐switching of valves and on/off‐switching control of compressors in a gas network modelled by a graph with simplified euler equations on edges and suitable coupling conditions at nodes. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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