2012/10/25 by María Barbero-Liñán, Barbero-Liñán, María, Miguel C. Muñoz‐Lecanda +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microtubule and mitosis dynamics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1210.6762
openalex publication_date 2012/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An optimal control problem associated with the dynamics of the orientation of a bipolar molecule in the plane can be understood by means of tools in differential geometry. For first time in the literature k-symplectic formalism is used to provide the optimal control problems associated to some families of partial differential equations with a geometric formulation. A parallel between the classic formalism of optimal control theory with ordinary differential equations and the one with particular families of partial differential equations is established. This description allows us to state and prove Pontryagin's Maximum Principle on k-symplectic formalism. We also consider the unified Skinner-Rusk formalism for optimal control problems governed by an implicit partial differential equation.