Learning the Globally Optimal Distributed LQ Regulator
Abstract
We study modelfree learning methods for the outputfeedback Linear Quadratic (LQ) control problem in finitehorizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed control and present a significant challenge in the sense that standard modelbased optimization and learning leads to intractable numerical programs in general. Building upon recent results in zerothorder optimization, we establish modelfree samplecomplexity bounds for the class of distributed LQ problems where a local gradient dominance constant exists on any sublevel set of the cost function. %which admit a local gradient dominance constant valid on the sublevel set of the cost function. We prove that a fundamental class of distributed control problems  commonly referred to as Quadratically Invariant (QI) problems  as well as others possess this property. To the best of our knowledge, our result is the first samplecomplexity bound guarantee on learning globally optimal distributed outputfeedback control policies.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.08774
 Bibcode:
 2019arXiv191208774F
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Optimization and Control
 EPrint:
 Soon to appear in Proceedings of Machine Learning Research, Vol. 120. Presented at L4DC 2020