A Laguerre homotopy method for optimal control of nonlinear systems in semi-infinite interval

TL;DR

This paper introduces a Laguerre homotopy method (LaHOC) for solving nonlinear optimal control problems on semi-infinite intervals, demonstrating improved accuracy and efficiency over existing methods.

Contribution

The paper develops a novel Laguerre homotopy approach using spectral analysis for nonlinear control problems, with proven local convergence and superior numerical performance.

Findings

LaHOC outperforms Matlab BVP5C in accuracy.

LaHOC is more efficient than existing methods.

Numerical results confirm LaHOC's effectiveness.

Abstract

This paper presents a Laguerre homotopy method for optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagins maximum principle. A proof of local convergence of the LaHOC is provided. Numerical comparisons are made between the LaHOC, Matlab BVP5C generated results and results from literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency.