A Computational Method for Solving Optimal Control Problem of Time-varying Singular Systems Using the Haar Wavelets

This paper deals with the implementation of Haar wavelets to solve the optimal control problem of linear time-varying singular systems with a quadratic cost functional. The properties of Haar Wavelets are presented. The state variable, state rate and the control vector are expanded in Haar orthogonal basis with unknown coefficients. The relation between the coefficients of the state rate and state variable is provided and the necessary condition of optimality is derived as a linear system of algebraic equations in terms of the unknown coefficients of the state and control vectors. Illustrative example is included to demonstrate the validity and applicability of the technique.