Approximation method for singular LQ problem for a class of singular systems with time-delay

An approximation method for solving singular linear quadratic (LQ) optimal control problem for a class of singular systems with time-delay is investigated. First, based on the algebra equivalent transformation, the original singular LQ problem is transformed into a nonsingular LQ problem for standard systems with time-delay. Then, by using perturbation method to solve the nonsingular LQ problem, the optimal control law of the original nonsingular LQ problem is obtained. The control law consists of state feedback term and a time-delay compensation term which is a series sum of adjoint vectors. The compensation term can be approximately obtained by a recursion formula of adjoint vectors.