Numerical solution of optimal control of time-varying singular systems via operational matrices

In this paper, a numerical method for solving the constrained optimal control of time-varying singular systems with quadratic performance index is presented. Presented method is based on Bernstein polynomials. Operational matrices of integration, differentiation and product are introduced and utilized to reduce the solution of optimal control problems with time-varying singular systems to the solution of algebraic equations set. The strength of the method is shown by exhibiting a numerical implementation using operational matrices that solves the determined control problem by solving an equation set. The method converges rapidly to the exact solution and gives very accurate results even by low value of . Illustrative examples are included to demonstrate the validity and efficiency of the technique and convergence of method to the exact solution especially for unstable singular systems.