Symplectic Runge–Kutta discretization of a regularized forward–backward sweep iteration for optimal control problems
Xin Liu, Jason Frank
Abstract
Li et al. (2018) have proposed a regularization of the forward–backward sweep iteration for solving the Pontryagin maximum principle in optimal control problems. The authors prove the global convergence of the iteration in the continuous time case. In this article we show that their proof can be extended to the case of numerical discretization by symplectic Runge–Kutta pairs. We demonstrate the convergence with a simple numerical experiment.
Topics & Concepts
MathematicsDiscretizationRunge–Kutta methodsSymplectic geometryOptimal controlRegularization (linguistics)Convergence (economics)Applied mathematicsNumerical analysisMathematical analysisMathematical optimizationComputer scienceArtificial intelligenceEconomic growthEconomicsNumerical methods for differential equationsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and Aerodynamics