A new approach for solving infinite horizon optimal control problems using Laguerre functions and Ritz spectral method

ABSTRACT

In this paper, a new numerical scheme is constructed to solve a class of Infinite Horizon Optimal Control Problems (IHOCPs). The idea is to extend the spectral Ritz method to solve an IHOCP directly by a proper approximation of the state and control functions. We solve the IHOCP on the original time interval. Applying the new constructed operational Laguerre matrix and substituting the estimated functions into the performance index yields a system of algebraic equations. Notably, the choice of Laguerre polynomials along with the spectral Ritz method provides to impose all the given initial and boundary conditions easily. By rigorous proofs, the convergence of the new method is investigated. The numerical technique is also examined by adding three illustrative application problems to show the applicability and effectiveness of the proposed technique. Furthermore, our results are compared with the outlets of other works to show superiority of the proposed methodology.

KEYWORDS:

• Infinite horizon optimal control problems (IHOCPs)
• spectral Ritz method
• laguerre polynomial
• convergence
• multivariable optimization

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 76M22
• 49J15
• 33C45

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

K. Mamehrashi http://orcid.org/0000-0003-3663-2424

A. Nemati http://orcid.org/0000-0002-1263-345X