Optimal Control for Descriptor Systems: Tracking Problem (RESEARCH NOTE)

Singular systems have been studied extensively during the last two decades due Abstract to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associated tr ajectory. Two methods are presented for solving these trajectories. The first method uses the concept of the Drazin inverse, and the second involves the derivation and solution of a Riccati equation. Similar to the linear regulator problem, necessary and sufficient conditions for existence and uniqueness of a solution are stated.