What question did this study set out to answer?

The aim is to determine feedback gain for shaping the controllability Gramian in control systems.

Controller Design for Controllability Gramian Shaping via Manifold Optimization

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Randomized trial demonstrates optimization of controllability Gramian in control systems, suggesting effective feedback gain determination.

The aim is to determine feedback gain for shaping the controllability Gramian in control systems.
Formulated feedback gain determination as an optimization problem on a manifold with equality constraints.
Defined controllability Gramian based on feedback gain for application in stable and unstable systems.
Compared the proposed method with H2 control theory.
Demonstrated effectiveness of the proposed method through two examples.
Highlighted similarities and differences between Gramian shaping and H2 control approaches.

Nishimoto et al. (2026) studied this question.

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Randomized trial demonstrates optimization of controllability Gramian in control systems, suggesting effective feedback gain determination.