Optimal Control for a Class of Interconnected Discrete-Time Systems with Parameter Uncertainty

A large-scale interconnected discrete-time system is considered. This system consists of three interconnected discrete-time subsystems x1, X2, and X3 where x2 and X3 can be directly controlled with the controls u2 and u3 respectively while x1 is being controlled through the subsystems X2 and X3. Also it is assumed that the subsystem x1 has an uncertain parameter. In the following, controls u2 and u3 are designed such that a given cost functional and also the sensitivity of the system with respect to the uncertain parameter is minimized.