SUBOPTIMAL CONTROL OF LINEAR DELAY SYSTEMS VIA LEGENDRE SERIES

A method for finding the suboptimal control of linear delay systems wi th a quadratic cost functional using Legendre series is discussed. The state variable, state delay, state rate, and the control vector are e xpanded in the shifted Legendre series with unknown coefficients. The relation between the coefficients of the state rate with state variabl e is provided and the necessary condition of optimality is derived as a linear system of algebraic equations. A numerical example is include d to demonstrate the validity and the applicability of the technique.