Efficient Learning of Distributed Linear-Quadratic Controllers

Abstract

In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed controllers can be learned with sub-linear sample complexity and computed with near-linear time complexity, both measured with respect to the dimension of the system. In particular, we provide sharp end-to-end guarantees on the stability and the performance of the designed distributed controller and prove that for sparse systems, the number of samples needed to guarantee robust and near optimal performance of the designed controller can be significantly smaller than the dimension of the system. Finally, we show that the proposed optimization problem can be solved to global optimality with near-linear time complexity by iteratively solving a series of small quadratic programs.

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Cited by in corpus (7)

• Learning the Globally Optimal Distributed LQ Regulator
• Model-Free Practical Cooperative Control for Diffusively Coupled Systems
• Distributed Online Linear Quadratic Control for Linear Time-invariant Systems
• Monitoring Link Faults in Nonlinear Diffusively-coupled Networks
• Learning Partially Observed Linear Dynamical Systems from Logarithmic Number of Samples
• Graph Neural Networks for Distributed Linear-Quadratic Control
• Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM