Data-Driven Structured Control for Continuous-Time LTI Systems
Zhaohua Yang, Yuxing Zhong, Ling Shi
TL;DR
The paper addresses data-driven design of structured controllers for continuous-time LTI systems with unknown dynamics $(A,B)$. It constructs a minimal matrix ellipsoid $\Phi$ to enclose all system matrices consistent with collected data and bounded disturbance, and then develops SDP-based linearizations to enforce a prescribed sparsity pattern $K\in S$ for three objectives: stabilization, $H_2$, and $H_\infty$ performance. An iterative algorithm alternates between solving relaxed SDPs and updating the structured gain to achieve recursive feasibility and reduced structure violation, outperforming prior discrete-time approaches in feasibility under data noise. Simulations on a mass-spring chain illustrate effective stabilization and performance bounds under varying data lengths and disturbance levels, highlighting practical impact for continuous-time data-driven control with structure constraints.
Abstract
This paper addresses the data-driven structured controller design problem for continuous-time linear time-invariant (LTI) systems. We consider three control objectives, including stabilization, $H_2$ performance, and $H_\infty$ performance. Using the collected data, we construct a minimal matrix ellipsoid that contains all admissible system matrices. We propose some linearization techniques that enable us to incorporate the structural constraint on the controller, which motivates an iterative algorithm for each control objective. Finally, we provide some numerical examples to demonstrate the effectiveness of the proposed methods.