Abstract
Infinite-dimensional perturbations in all constraints of an optimal control problem governed by a Volterra integral equation with the presence of a state constraint are considered. These perturbations give rise to a value function, whose analysis through the proximal normal technique provides sensitivity, controllability, and even necessary conditions for the basic problem. Actually all information about the value function is contained in Clarke's normal cone of its epigraph, which can be characterized by the proximal normal formula.
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Yezza, A. Sensitivity, controllability, and necessary conditions of optimal control problems governed by integral equations. Appl Math Optim 32, 73–97 (1995). https://doi.org/10.1007/BF01189904
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DOI: https://doi.org/10.1007/BF01189904
Key words
- Optimal control
- State constraint
- Volterra integral equation
- Necessary conditions
- Controllability
- Sensitivity
- Value function
- Proximal normal analysis
- Proximal analysis