Optimal control of singular systems via legendre series

A method for finding the optimal control of linear singular systems with a quadratic cost functional using Legendre series is discussed. The state var iable, state rate, and the control vector are expanded in the shifted Legen dre series with unknown coefficients. The relation between the coefficients of the state rate with state Variable is provided and the necessary condit ion of optimality is derived as a system of algebraic equations. A numerica l example is included to demonstrate the validity and the applicability of the technique.