Optimal preview control for a class of continuous time-invariant descriptor systems

This paper presents the optimal finite horizon linear-quadratic control for a class of continuous linear time-invariant descriptor systems subject to a previewable desired output. For a quadratic performance index and a giving reference sequence, the solution is obtained in four steps. First, the continuous-time descriptor systems with previewable desired tracking signals are transformed into augmented error descriptor systems. Then, the necessary optimality conditions are derived from the maximum principle. Finally, the necessary optimality conditions can be transformed into differential Riccati equation by performing singular value decomposition of Ez. Subsequently, the solution of the differential Riccati equation can be obtained by solving the algebraic Riccati equation and the differential Lyapunov equation. The effectiveness and validity of the proposed approach have been demonstrated by an example.