A convex variational principle for the necessary conditions of classical optimal control

Amit Acharya; Janusz Ginster

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arXiv · 2502.15973

A convex variational principle for the necessary conditions of classical optimal control

Amit Acharya·Janusz Ginster

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Abstract

A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary differential equations (ODE) in a well-defined sense. The scheme is applied to the Quadratic-Quadratic Regulator problem for which an explicit form of the functional is derived, and existence of minimizers of the variational principle is rigorously shown. It is shown that the Linear-Quadratic Regulator problem with time-dependent forcing can be solved within the formalism without requiring any nonlinear considerations, in contrast to the use of a Riccati system in the classical methodology. Our work demonstrates a pathway for solving nonlinear control problems via convex optimization.

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Amit Acharya, Janusz Ginster. 2025-02-21. A convex variational principle for the necessary conditions of classical optimal control. https://arxiv.org/abs/2502.15973

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