APPLICATION OF LEGENDRE SERIES TO THE CONTROL-PROBLEMS GOVERNED BY LINEAR PARABOLIC EQUATIONS

A method for finding the optimal control problems governed by linear p arabolic equations using Legendre series is discussed. The optimal con trol of the one-dimensional diffusion equation is simplified into opti mal control of linear system with a quadratic cost functional. The sta te variable, state rate and the control vector are expanded in the shi fted Legendre series with unknown coefficients. The relation between t he coefficients of the state rate and control vector with state variab le is provided and the necessary condition of optimality is derived as a linear system of linear algebraic equations in terms of the unknown coefficient of the state vector. A numerical example is included to d emonstrate the validity and the applicability of the technique.