Year: 2022
Type: preprint
Abstract: The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent quantification of the closed-loop performance. Recent developments in model-free policy optimization for Linear Quadratic Gaussian (LQG) control have highlighted the importance of this question. In this paper, we first propose a new set of sufficient conditions ensuring that a perturbed controller remains internally stabilizing. Based on this result, we illustrate how to perform order reduction of general non-observer based controllers using balanced truncation and modal truncation. We also provide explicit bounds on the LQG performance of the reduced-order controller. Furthermore, for single-input-single-output (SISO) systems, we introduce a new controller reduction technique by truncating unstable modes. We illustrate our theoretical results with numerical simulations. Our results will serve as valuable tools to design direct policy search algorithms for control problems with partial observations.
Source: arXiv (Cornell University)
Authors: Ren, Zhaolin, Zheng, Yang, Fazel, Maryam, Li, Na
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: Collaborative Research: MLWiNS: Distributed Learning over Multi-Access Channels: From Bandlimited Coordinate Descent to Gradient Sketching, Matrix Decomposition for Scalable Conic Optimization with Applications to Distributed Control and Machine Learning, G2000835420, TRIPODS+X:EDU: Foundational Training in Neuroscience and Geoscience via Hackweeks, CIF: Small: Online Learning and Optimal Experiment Design with a Budget, G4375494504, TRIPODS: Institute for Foundations of Data Science, G5972442391, AI Institute in Dynamic Systems, Collaborative Research: CIF: Medium: MoDL:Toward a Mathematical Foundation of Deep Reinforcement Learning, G8876996369
OpenAlex ID: W4310513466