Numerical simulation of fractional order optimal control problem

Abstract

A simple and straightforward numerical method based on reflection operator is proposed in this paper for solving an optimal control problem (OCP) of continuous- time fractional order singular system (FOSS) with fixed final state end point condition by keeping final time fixed. Singular system (SS) dynamics is described by the fractional order differential equations (FDEs) in the sense of either Riemann-Liouville fractional derivative (RLFD) or Caputo fractional derivative (CFD). By using reflection operator we convert right RLFD to its equivalent left RLFD and then approximate the necessary conditions using Grünwald-Letnikov approximation (GLA). An example is illustrated to check the efficacy of proposed algorithm.

Subject Classification:

• 49M05
• 26A33

Keywords:

• Fractional optimal control
• Riemann-Liouville derivative
• Grünwald-Letnikov approximation
• Fractional order singular system
• Caputo derivative