Feedback-invariant optimal control theory and differential geometry—I. Regular extremals (original) (raw)

This paper introduces a feedback-invariant framework for optimal control theory, focusing on regular extremals and their geometric underpinnings. It begins with the definition of an L-derivative for infinite-dimensional control systems, defines smooth control systems with associated boundary-value mappings, and establishes critical points corresponding to extremal trajectories. Key concepts such as Jacobi curves in the Lagrangian Grassmannian and their relations to curvature and conjugate points are explored. The findings aim to extend Hamiltonian dynamics to nonstationary Hamiltonians while maintaining symplectic structure, providing a foundation for future research in optimal control and differential geometry.