ABSTRACT
This chapter discusses some basic definitions and a simple variational problem of extremizing a functional. It examines the plant as a conditional optimization problem and also discusses various types of problems based on the boundary conditions. Calculus of variations (CoV) or variational calculus deals with finding the optimum value of a functional. The variation plays the same role in determining optimal value of a functional as the differential does in finding extremal or optimal value of a function. The chapter describes the optimal control system by variational techniques, and in the process introduce the Hamiltonian function, which was used by Pontryagin and his associates to develop the famous Minimum Principle. It considers the optimal control system where the performance index is of general form containing a final cost function in addition to the integral cost function.
