Geodesic
Optimal control with connected initial and terminal conditions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 13-28

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An optimal control problem with linear dynamics is considered on a fixed time interval. The ends of the interval correspond to terminal spaces, and a finite-dimensional optimization problem is formulated on the Cartesian product of these spaces. Two components of the solution of this problem define the initial and terminal conditions for the controlled dynamics. The dynamics in the optimal control problem is treated as an equality constraint. The controls are assumed to be bounded in the norm of $\mathrm L_2$. A saddle-point method is proposed to solve the problem. The method is based on finding saddle points of the Lagrangian. The weak convergence of the method in controls and its strong convergence in state trajectories, conjugate trajectories, and terminal variables are proved.
Keywords: terminal control, boundary value problems, convex programming, Lagrange function, solution methods
Mots-clés : convergence. 
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     author = {A. S. Antipin and E. V. Khoroshilova},
     title = {Optimal control with connected initial and terminal conditions},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a1/}
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A. S. Antipin; E. V. Khoroshilova. Optimal control with connected initial and terminal conditions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 13-28. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a1/