Data-Driven Stabilization of Unknown Linear-Threshold Network Dynamics

2025/04/28 by Xuan Wang, Wang, Xuan, Duy Duong‐Tran +3
Computer Science · Engineering · #Control Systems and Identification #FOS: Electrical engineering #Neural Networks Stability and Synchronization #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2504.19950

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies the data-driven control of unknown linear-threshold network dynamics to stabilize the state to a reference value. We consider two types of controllers: (i) a state feedback controller with feed-forward reference input and (ii) an augmented feedback controller with error integration. The first controller features a simpler structure and is easier to design, while the second offers improved performance in the presence of system parameter changes and disturbances. Our design strategy employs state-input datasets to construct data-based representations of the closed-loop dynamics. Since these representations involve linear threshold functions, we rewrite them as switched linear systems, and formulate the design problem as that of finding a common controller for all the resulting modes. This gives rise to a set of linear matrix inequalities (LMIs) whose solutions corresponds to the controller gain matrices. We analyze the computational complexity of solving the LMIs and propose a simplified, sufficient set of conditions that scales linearly with the system state. Simulations on two case studies involving regulation of firing rate dynamics in rodent brains and of arousal level dynamics in humans demonstrate the effectiveness of the controller designs.

Citations

• Efficient Reconstruction of Neural Mass Dynamics Modeled by Linear-Threshold Networks
• Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey
• The informativity approach to data-driven analysis and control
• Data-driven dissipativity analysis: application of the matrix S-lemma
• Designing Experiments for Data-Driven Control of Nonlinear Systems
• Data-driven stabilization of nonlinear polynomial systems with noisy data
• Learning nonlinear dynamical systems from a single trajectory
• Data-Driven Model Predictive Control with Stability and Robustness Guarantees
• Formulas for Data-driven Control: Stabilization, Optimality and\n Robustness
• Data-Enabled Predictive Control: In the Shallows of the DeePC
• Hierarchical Selective Recruitment in Linear-Threshold Brain Networks,\n Part II: Multi-Layer Dynamics and Top-Down Recruitment
• Hierarchical Selective Recruitment in Linear-Threshold Brain Networks, Part I: Single-Layer Dynamics and Selective Inhibition
• Fixed points of competitive threshold-linear networks
• MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications
• ImageNet classification with deep convolutional neural networks
• Data-Driven Model-Free Adaptive Control for a Class of MIMO Nonlinear Discrete-Time Systems
• Opinion Dynamics with Decaying Confidence: Application to Community Detection in Graphs
• The saturation threshold of public opinion: are aggressive media campaigns always effective?
• Hyperpolarization-Activated Cation Currents: From Molecules to Physiological Function

Related

• Stabilization of Nonlinear Systems with State-Dependent Representation: From Model-Based to Direct Data-Driven Control
• Event-triggered Control From Data
• Formulas for Data-driven Control: Stabilization, Optimality and\n Robustness
• Designing Experiments for Data-Driven Control of Nonlinear Systems
• Data-driven nonlinear output regulation via data-enforced incremental passivity