ABSTRACT
This chapter describes a unified approach via block-pulse functions (BPF) or shifted Legendre polynomials (SLP) are presented to solve the optimal control problem of linear time-invariant systems by integro-differential equations. By using the elegant operational properties of orthogonal functions (OF), computationally elegant algorithms are developed for calculating optimal control law and state trajectory of dynamical systems. Synthesis of optimal control law for deterministic systems described by the integro-differential equations has been investigated via the dynamic programming approach. Subsequently, this problem has been studied via OF approach. Subsequently, optimal control problem has been studied via OF approach. The chapter deals with the optimal control problem and includes a numerical example.
