H2H2 control of preview systems

The H2H2-optimal controller for systems with preview, in which the knowledge of external input is available in advance for the controller, is derived. The single input case is first considered and solved by transforming the problem into a non-standard LQR problem. Based on the single input result, the multiple inputs case and the multiple preview times case are treated. In every case considered, the controller consists of a static state feedback plus a finite impulse response block. The paper also provides a formula for the optimal H2H2-norm that clearly shows how the performance gain owing to the previewed input varies as the preview time increases.