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

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