Singular H∞ Suboptimal Control for a Class of Nonlinear Cascade Systems

In the present paper singular state feedback H"~ suboptimal control for a class of nonlinear cascade systems is addressed. Under the assumption that a regular state feedback H"~ suboptimal control problem is solvable for a particular subsystem of the cascade system, an auxiliary nonlinear system is defined. It is shown that a state feedback solution to the singular H"~ suboptimal control problem for the auxiliary system also applies to the original problem. The advantage of the auxiliary problem to the original problem is that the auxiliary penalty variable has lower dimension than the original penalty variable. It is shown how this fact can simplify the problem considerably for the case when the auxiliary system can be strongly input-output decoupled. The theory is applied to a problem of a rigid spacecraft with actuator dynamics. Application to the special case when a subsystem of the nonlinear cascade system is passive is also considered.