Disturbance attenuation in hyperbolic 2D-systems
We consider disturbed linear 2D-systems of Fornasini-Marchesini type in the continuous time case. These systems are also named Goursat-type systems. Conditions for unique solvability of the disturbed optimal control problem with a quadratic cost functional are obtained. The disturbed or worst case optimal control guarantees to minimize the cost functional for any unknown disturbance input. In a second part then we consider a disturbance attenuation by boundary controls, i.e., by using the Goursat-data as control functions. In the 2D-case this results in two control functions acting independently on the system. We study a cooperative and a non-cooperative situation. In the cooperative situation we again obtain a disturbed optimal control problem and get conditions for existence and uniqueness of such a disturbed optimal control problem. If the action of the agents is non-cooperative we assume that it is agreed that they act on an open-loop Nash/worst-case equilibrium strategy. Sufficient conditions for the existence of such an equilibrium are obtained.
disturbance attenuation disturbed optimal control open-loop nash/worst-case equilibrium 2d continuous time systems linear systems disturbed systems robust control quadratic performance index