Exact Bang-Bang Optimal Control for Problems with Nonlinear Costs
In  a general functional-analytic theory of “existence without convexity” was developed and applied to control and variational problems. Apart from being fundamental, this theory also leads to an extension of classical existence results in very concrete cases, because of its systematic incorporation of concavity — instead of classical linearity — for the trajectory cost function. Here the theory is shown to apply also to bang-bang optimal control, for which, likewise, (i) a comprehensive treatment is given and (ii) all classical results are shown to be extendible by the incorporation of a concave trajectory cost function.
KeywordsLower Semicontinuous Control Pair Lower Semi Abstract Existence Linear Integral Operator
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