Closed-form solution of optimal control problem of a fractional order system

Abstract

A formulation and an analytical solution technique of fractional optimal control problem (FOCP) is presented in this paper. The performance index (PI) considered is a conformable fractional integral (CFI) function and is a function of both the state and the control variables. Dynamic behaviour of the system is described by conformable fractional differential equation (FDE). The necessary conditions of optimality and the general transversality condition in terms of Hamiltonian are obtained using variational approach. Both the fixed and free final end point conditions have been considered. An analytical solution technique is presented for solving the conformable FOCPs. To validate the formulation and solution scheme numerical examples are presented.