Finite-Horizon H∞ Control Problem with Singular Control Cost

For linear uncertain systems, we consider a finite-horizon H-infinity control problem. A weight matrix of the control cost in the functional of this problem is singular. In this case, the Riccati equation approach is not applicable to solution of the considered H-infinity problem, meaning that it is singular. To solve this problem, a regularization method is proposed. Namely, the original problem is associated with a new H-infinity control problem for the same dynamics, while with a new functional. The weight matrix of the control cost in the new functional is a nonsingular parameter-dependent matrix, which becomes the original weight matrix for zero value of the parameter. For all sufficiently small values of this parameter, the new H-infinity control problem is regular, and it is a partial cheap control problem. Using its asymptotic analysis, a controller solving the original singular H-infinity control problem is designed. An illustrative example is presented.