多様体上の最適化を用いた可制御性グラミアン整形のための制御器設計

抄録

This paper presents a feedback gain determination method for shaping the controllability Gramian with manifold optimization. We define a controllability Gramian that depends on the feedback gain, enabling it to be used in both stable and unstable systems. The controller design is then formulated as shaping this Gramian to achieve a desired input-state relationship. This study shows that the proposed method can be formulated as an optimization on a manifold with equality constraints. We also compare the Gramian shaping and the disturbance rejection control, such as H₂ control, and discuss the similarities and differences between the proposed method and the H₂ control approach. Finally, two examples demonstrate the effectiveness of the proposed method.