Publication details

Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions

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Year of publication 2021
Type Article in Periodical
Magazine / Source ESAIM: Control, Optimisation and Calculus of Variations
MU Faculty or unit

Faculty of Science

Keywords Optimal control problem; joint (coupled) endpoints; separated endpoints; controllability; strong Pontryagin principle; coercivity; sensitivity analysis; free time problem
Description In this paper we develop a new approach for optimal control problems with general jointly varying state endpoints (also called coupled endpoints). We present a new transformation of a nonlinear optimal control problem with jointly varying state endpoints and pointwise equality control constraints into an equivalent optimal control problem of the same type but with separately varying state endpoints in double dimension. Our new transformation preserves among other properties the controllability (normality) of the considered optimal control problems. At the same time it is well suited even for the calculus of variations problems with joint state endpoints, as well as for optimal control problems with free initial and/or final time. This work is motivated by the results on the second order Sturm–Liouville eigenvalue problems with joint endpoints by Dwyer and Zettl (1994) and by the sensitivity result for nonlinear optimal control problems with separated state endpoints by the authors (2018).
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