Interval-oriented reduced-order model for uncertain control systems

The reduced-order model (ROM), as a crucial research avenue in control system design, effectively simplifies complexity and enhances computational efficiency when handling high-dimensional models. However, considering the presence of uncertainties caused by the incompleteness of the system model and the errors induced by sensors, conventional probabilistic methods rely on a substantial number of samples and may struggle to be applicable when there is an insufficient quantity of samples available. To address this challenge, this paper presents an interval-oriented reduced-order model (IROM) tailored for uncertain linear systems, aiming to improve the accuracy of the uncertain reduced-order model under small-sample conditions. Based on the unknown but bounded parameters, the interval state-space equations are established, and transformed into interval balanced equations. The uncertainty bounds for controllability and observability matrices, as well as Hankel singular values, are obtained via interval Lyapunov equations and an interval perturbation-based singular value decomposition method. Considering the dense distributions of uncertain Hankel singular values, a novel interval truncation criterion is introduced to determine the reduced model order. After order selection using the optimization method, the reduced-order models and output predictions can be obtained. Two application examples are provided to demonstrate the accuracy and efficiency of the developed methodology.