Linear Quadratic Optimal Control Problem of Fractional Order Continuous – Time Singular System

Abstract

In this paper, formulation and an approximated numerical scheme for linear quadratic optimal control problem (LQOCP) of fractional order singular system (FOSS) with fixed final time in the sense of Riemann-Liouville (RL) fractional derivative (FD) is considered. Quadratic form of performance index (PI) is considered. The solution of singular system (SS) is difficult because of its complex nature. Therefore, we convert the FOSS into the standard fractional order system (SFOS) and then obtain the necessary conditions using Lagrange multiplier approach. Thereafter, for solving the necessary conditions, fractional differential equations (FDEs) are approximated using the Grünwald–Letnikov approximation (GLA). An example is illustrated to demonstrate the applicability of the formulation and solution scheme.