Approximated numerical solution of fixed final time optimal control problem of fractional order continuous - Time singular system

Formulation and approximated numerical solution of fixed final time and fixed final state optimal control problem (OCP) of fractional order singular system (FOSS) in the sense of Caputo derivative is presented in this paper. General form of performance index (PI) is considered. Singular systems (SSs) are complex in nature. Due to this, solution is difficult. Therefore, first we transform FOSS into the standard fractional order system (SFOS) using coordinate transformation and then obtain the optimal necessary conditions. Approximated numerical solution of necessary conditions is obtain by using Grünwald–Letnikov approximation (GLA) based numerical method. In order to demonstrate the applicability of the formulation and efficacy of solution method, an example is illustrated.