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In Hilbert space, we consider an optimal control problem based on linear dynamics that transfers the system from the initial state to the final state. The initial and final states are implicitly specified as solutions to convex programming problems. A saddle point solution method based on the Lagrangian formalism and duality theory is proposed. Its convergence to the solution of the problem is proven: strong in trajectories, conjugate trajectories and finite-dimensional variables of boundary value problems, and weak in controls.

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Asymptotic Convergence of Phase Trajectories in Linear Optimal Control Problems

  • 会议论文

  • 发表日期：

    2026年

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  • Anatoly Antipin,
  • Elena Khoroshilova

摘要

In Hilbert space, we consider an optimal control problem based on linear dynamics that transfers the system from the initial state to the final state. The initial and final states are implicitly specified as solutions to convex programming problems. A saddle point solution method based on the Lagrangian formalism and duality theory is proposed. Its convergence to the solution of the problem is proven: strong in trajectories, conjugate trajectories and finite-dimensional variables of boundary value problems, and weak in controls.