WIAS Preprint No. 3215, (2025)

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


Authors

  • Acharya, Amit
    ORCID: 0000-0001-8051-1668
  • Ginster, Janusz
    ORCID: 0000-0001-5825-1556

2020 Mathematics Subject Classification

  • 49J15 49J35 49J45

Keywords

  • Optimal control, convex variational formulation, quadratic-quadratic regulator

DOI

10.20347/WIAS.PREPRINT.3215

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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