Efficient computation of almost invisible inputs for linear input redundant systems

Overview & Synopsis

Input redundant systems have more inputs than needed to control the output and offer advantages such as fault tolerance and improved performance. However, identifying such redundant inputs in high-dimensional systems can be computationally intensive and is prone to inaccuracies. This article proposes an approach that uses model reduction by balanced truncation to simplify input redundancy analysis. By reducing the system order, we identify "invisible inputs" for the reduced-order model and design a reduced order state feedback mechanism to decouple them from the "visible inputs." Then, error bounds from balanced truncation provide guarantees for applying this decoupling to the original system, as a feedforward input. The approach offers significant computational savings, as demonstrated in numerical examples. I. INTRODUCTIONMany engineering and control systems are designed with more inputs than strictly necessary to control the system output [1], resulting in what is known as an input redundant (IR) system [2]. This redundancy offers several advantages, such as failure resilience, improved performance, and improved managing of the state-of-health [1], [3], [4], [5].A recent study has provided a comprehensive characterization of input redundancy in linear time-invariant (LTI) systems [2]. The approach relies on geometric control theory tools [6], particularly controlled-invariant and outputinvisible subspaces, which are central to the understanding of input redundancy. Controlled-invariant subspaces can be kept invariant using appropriate control inputs, meaning the state of the system remains within these subspaces once entered inside. This is achieved through state feedback, commonly referred to as a friend of the subspace, which plays a crucial role in the analysis and design of input redundant systems.While input redundancy provides significant benefits, adding extra inputs also increases the complexity of system analysis and control. Identifying which inputs are redundant becomes essential for reducing complexity and improving system efficiency, especially in large-scale systems like batteries, multicell converters, and supercapacitor systems [7], [8], [9]. In such cases, applying the characterization from [2], however, presents significant computational challenges. In particular, the computation of the controlledinvariant, output-invisible subspaces, and the friend neces-J.Kreiss and M. Jungers are with