H2 Optimal Control in a Behavioral Framework
Osamu KANEKO, Takashi DOI, Takao FUJII
In this paper, we address H2 optimal control problem in a behavioral framework. Firstly, we formalize H2 optimal control problem addressed here under some assumptions. Secondly, we provide a necessary and sufficient condition for a control law to be admissible : namely, it guarantees the nonrestrictiveness of the disturbance and the boundedness of H2 norm of the transfer function from disturbance variables to regulated ones as well as the stability of the interconnected system. Thirdly, we provide a necessary and sufficient condition for a control law to be H2 optimal : namely, it is an admissible control law and minimizes H2 norm of the transfer function from disturbance variables to regulated ones after the interconnection. By using this condition, we also provide a parameterization of H2 optimal control laws and then a concrete algorithm for obtaining them. Finally, an illustrative example is also given in order to show the effectiveness of our result.