Abstract: This paper aims at solving the linear-quadratic optimal control problems ( LQOCP) for time-varying descriptor systems in a real Hilbert space. By using the Moore-Penrose inverse theory and space decomposition technique, the descriptor system can be rewritten as a new differential-algebraic equation (DAE), and then some novel sufficient conditions for the solvability of LQOCP are obtained. Especially, the methods proposed in this work are simpler and easier to verify and compute, and can solve LQOCP without the range inclusion condition. In addition, some numerical examples are shown to verify the results obtained.

Key words: linear-quadratic optimal control problem (LQOCP), time-varying descriptor system, Moore-Penrose inverse, space decomposition