Abstract
This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx′(t)=Ax(t) + f(t, x(t), u(t)), u(t) ε U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.
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Communicated by S. K. Mitter
Work (partially) supported by the Research Project “Equazioni di evoluzione e applicazioni fisicomatematiche” (M.U.R.S.T.-Italy).
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Cannarsa, P., Frankowska, H. Value function and optimality conditions for semilinear control problems. Appl Math Optim 26, 139–169 (1992). https://doi.org/10.1007/BF01189028
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DOI: https://doi.org/10.1007/BF01189028
Key words
- Optimal control
- Distributed parameter systems
- Dynamic programming
- Optimality conditions
- Strongly continuous semigroups
- Nonsmooth analysis