Optimal Control of Nonlinear Fredholm Integral Equations |
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Authors: | Roubí?ek T |
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Institution: | (1) Mathematical Institute, Charles University, Prague, and Institute of Information Theory and Automation, Academy of Sciences, Prague, Czech Republic |
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Abstract: | Optimal control problems with nonlinear equations usually do not possess optimal solutions, so that their natural (i.e., continuous) extension (relaxation) must be done. The relaxed problem may also serve to derive first-order necessary optimality condition in the form of the Pontryagin maximum principle. This is done here for nonlinear Fredholm integral equations and problems coercive in an L
p-space of controls with p<+ . Results about a continuous extension of the Uryson operator play a key role. |
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Keywords: | Nonlinear integral equations optimal control in L
p-spaces relaxation existence stability nonconcentration optimality conditions Pontryagin maximum principle |
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