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.
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- E.J. Balder, Existence results by extremal properties of the original controls, unpublished preprint, 1978.Google Scholar
- E.J. Balder, New existence results for optimal controls in the absence of convexity: the importance of extremality, forthcoming.Google Scholar
- H. Berliocchi and J.-M. Lasry, Intégrandes normales et mesures paramétrées en calcul des variations, Bull. Soc. Math. France 101 (1973), 129–184.Google Scholar
- A. Cellina and G. Colombo, On a classical problem of the calculus of variations without convexity assumptions, Ann. Inst. H. Poincaré, Analyse Nonlinéaire 7 (1989), 97–106.Google Scholar
- L. Cesari, Optimization Theory and Applications: Problems with Ordinary Differential Equations, Springer-Verlag, Berlin, 1983.Google Scholar
- G. Choquet, Lectures on Analysis, Benjamin, Reading, Mass., 1969.Google Scholar
- H. Hermes and J.P. Lasalle, Functional Analysis and Time Optimal Control, Academic Press, New York, 1969.Google Scholar
- R.K. Miller, Nonlinear Volterra Integral Equations, Benjamin, Menlo Park, California, 1971.Google Scholar
- J.-P. Raymond, Conditions nécessaires et suffisantes d’existence de solutions en calcul des variations, Ann. Inst. H. Poincaré, Analyse non linéaire 4 (1987), 169–202.Google Scholar
- J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972.Google Scholar