Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications

Emilio Molina (), Alain Rapaport () and Héctor Ramírez ()
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Emilio Molina: Universidad de Chile
Alain Rapaport: Université Montpellier
Héctor Ramírez: Universidad de Chile

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 3, No 9, 953-975

Abstract: Abstract We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples.

Keywords: Optimal control; Maximum cost; Mayer problem; State constraint; Differential inclusion; Numerical schemes; SIR model; 49N90; 49J35; 49J45; 65K10; 90-08 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02094-z

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