Псевдо-оптимальное решение вариационной задачи со свободным правым концом и заданным временем окончания переходного процесса

Автоматика и телемеханика. 2025. № 10. С. 3–20.

Afanasiev V.

The optimal control of a system’s final state is a fundamental problem that constitutes the core of many optimization tasks. Such problems involve describing the dynamic object, specifying constraints on controls and states, and defining a quality functional, typically a Bolza functional. The necessary optimality conditions for synthesizing the corresponding controls are written as a canonical Euler–Lagrange system with specified boundary conditions.
Synthesizing these controls requires solving boundary value problems, which is usually achieved through numerical methods. This paper proposes an alternative approach to solving two-point boundary value problems based
on R. Bellman’s inverse optimality principle [11], which preserves the functional relationship between the components of the boundary value problem throughout the control interval. The theoretical results are confirmed through simulations of a system with synthesized control.

Keywords: оптимальное управление, Optimal control, Hamiltonian of the system, canonical Euler–Lagrange system, boundary conditions of the canonical system, Гамильтониан системы, Уравнение Эйлера-Лагранжа системы, краевые условия канонической системы