A Laguerre spectral method for quadratic optimal control of nonlinear systems in a semi-infinite interval

Abstract

This paper presents a Laguerre homotopy method for quadratic optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, the spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagin's 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 the literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency.

Keywords

• laguerre method
• collocation method
• optimal control problems
• spectral homotopy analysis method (sham)
• semi-infinite interval