Scalable Input Dimension Reduction for Large Systems With Guaranteed Controllability

ABSTRACT Controlling multi‐input large‐scale systems is a challenging task, as a high‐dimensional control input space may lead to increased computational demands, difficulties in controller design, and system‐wide time delays. In this paper, we propose a novel input dimension reduction method that transforms any linear time‐invariant multi‐input system into an input‐coupled nonlinear system with only two control inputs, thereby significantly reducing the dimensionality of the input space and is scalable. We demonstrate that the nonlinear system retains global controllability and certain stability properties under certain suitable assumptions. In addition, we propose straightforward design methods for the feedback gain matrix to globally stabilize the nonlinear system. Using numerical simulations, we verify the theoretical results and test the effectiveness of the input dimension reduction method under noise and time delay.