Sparsity in Partially Controllable Linear Systems

• URL: http://arxiv.org/abs/2110.06150v1
• Date: Tue, 12 Oct 2021 16:41:47 GMT
• Title: Sparsity in Partially Controllable Linear Systems
• Authors: Yonathan Efroni, Sham Kakade, Akshay Krishnamurthy, Cyril Zhang
• Abstract summary: We study partially controllable linear dynamical systems specified by an underlying sparsity pattern. Our results characterize those state variables which are irrelevant for optimal control.
• Score: 56.142264865866636
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable linear dynamical systems. However, in practice, we often encounter systems in which a large set of state variables evolve exogenously and independently of the control inputs; such systems are only \emph{partially controllable}. The focus of this work is on a large class of partially controllable linear dynamical systems, specified by an underlying sparsity pattern. Our main results establish structural conditions and finite-sample guarantees for learning to control such systems. In particular, our structural results characterize those state variables which are irrelevant for optimal control, an analysis which departs from classical control techniques. Our algorithmic results adapt techniques from high-dimensional statistics -- specifically soft-thresholding and semiparametric least-squares -- to exploit the underlying sparsity pattern in order to obtain finite-sample guarantees that significantly improve over those based on certainty-equivalence. We also corroborate these theoretical improvements over certainty-equivalent control through a simulation study.

Related papers

• Receding Hamiltonian-Informed Optimal Neural Control and State Estimation for Closed-Loop Dynamical Systems [4.05766189327054]
  Hamiltonian-Informed Optimal Neural (Hion) controllers are a novel class of neural network-based controllers for dynamical systems. Hion controllers estimate future states and compute optimal control inputs using Pontryagin's Principle.
  arXiv  Detail & Related papers  (2024-11-02T16:06:29Z)
• Controllability-Constrained Deep Network Models for Enhanced Control of Dynamical Systems [4.948174943314265]
  Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs and corresponding state observation outputs. We propose a control-theoretical method that explicitly enhances models estimated from data with controllability.
  arXiv  Detail & Related papers  (2023-11-11T00:04:26Z)
• Robust stabilization of polytopic systems via fast and reliable neural network-based approximations [2.2299983745857896]
  We consider the design of fast and reliable neural network (NN)-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty. We certify the closed-loop stability and performance of a linear uncertain system when a trained rectified linear unit (ReLU)-based approximation replaces such traditional controllers.
  arXiv  Detail & Related papers  (2022-04-27T21:58:07Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• Stable Online Control of Linear Time-Varying Systems [49.41696101740271]
  COCO-LQ is an efficient online control algorithm that guarantees input-to-state stability for a large class of LTV systems. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.
  arXiv  Detail & Related papers  (2021-04-29T06:18:49Z)
• Enforcing robust control guarantees within neural network policies [76.00287474159973]
  We propose a generic nonlinear control policy class, parameterized by neural networks, that enforces the same provable robustness criteria as robust control. We demonstrate the power of this approach on several domains, improving in average-case performance over existing robust control methods and in worst-case stability over (non-robust) deep RL methods.
  arXiv  Detail & Related papers  (2020-11-16T17:14:59Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Reinforcement Learning of Structured Control for Linear Systems with Unknown State Matrix [0.0]
  We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees. A special control structure enabled by this RL framework is distributed learning control which is necessary for many large-scale cyber-physical systems.
  arXiv  Detail & Related papers  (2020-11-02T17:04:34Z)
• Identifying Causal Structure in Dynamical Systems [6.451261098085498]
  We propose a method that identifies the causal structure of control systems. Experiments on a robot arm demonstrate reliable causal identification from real-world data.
  arXiv  Detail & Related papers  (2020-06-06T16:17:07Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.