A Hamiltonian Pertubation Approach to Construction of Geometric Integrators for Optimal Control Problems

  • M. D. S. AliyuEmail author
Short Communication


In this paper, we discuss computational methods for optimal control problems which preserve some geometric properties of the system. A Hamiltonian perturbation method is developed, which does not involve any discretization of either the cost function, or the dynamic equations. Instead, the approach relies mainly on an iterative successive approximation of the value-function, which converges uniformly to the solution. The approach is most effective when the Hamiltonian of the system is a polynomial function of the phase coordinates, and an example is presented to demonstrate this.


Optimal control Hamiltonian system Symplectic manifold Pontryagin’s minimum principle Generating function Hamilton–Jacobi equation Geometric integrator 



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© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringKing Faisal UniversityAl-AhsaSaudi Arabia

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