Singular Arcs in Optimal Periodic Controls for Scalar Dynamics and Integral Input Constraint

Thomas Guilmeau () and Alain Rapaport ()
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Thomas Guilmeau: Université Paris-Saclay, Inria, CentraleSupélec
Alain Rapaport: MISTEA, Université Montpellier, INRAE, Institut Agro

Journal of Optimization Theory and Applications, 2022, vol. 195, issue 2, No 7, 548-574

Abstract: Abstract We revisit recent results about optimal periodic control for scalar dynamics with input integral constraint, under lack of convexity and concavity. We show that in this more general framework, the optimal solutions are bang-singular-bang and generalize the bang-bang solutions for the convex case and purely singular for the concave one. We introduce a non-local slope condition to characterize the singular arcs. The results are illustrated on a class of bioprocesses models.

Keywords: Optimal control; Periodic control; Integral input constraint; Singular arc; 49J15; 49K15; 34C25; 49N20; 49J30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02095-y

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