On Regularizability and its Application to Online Control of Unstable LTI Systems

  title={On Regularizability and its Application to Online Control of Unstable LTI Systems},
  author={Shahriar Talebi and Siavash Alemzadeh and Niyousha Rahimi and Mehran Mesbahi},
  journal={IEEE Transactions on Automatic Control},
Learning, say through direct policy updates, often requires assumptions such as knowing a priori that the initial policy (gain) is stabilizing, or persistently exciting (PE) inputoutput data, is available. In this paper, we examine online regulation of (possibly unstable) partially unknown linear systems with no prior access to an initial stabilizing controller nor PE input-output data; we instead leverage the knowledge of the input matrix for online regulation. First, we introduce and… 

Figures from this paper

On the Sample Complexity of Stabilizing Linear Systems via Policy Gradient Methods

This paper proposes an explicit rule to adaptively adjust the discount factor by characterizing the stability margin using Lyapunov theory, which has independent interests of its own.

Online Stabilization of Unknown Networked Systems with Communication Constraints

This work proposes the first provably stabilizing algorithm, which uses a distributed version of nested convex body chasing to maintain a consistent estimate of the network dynamics and applies system level synthesis to determine a distributed controller based on this estimated model.



Online Regulation of Unstable Linear Systems from a Single Trajectory

The Data-Guided Regulator (DGR) synthesis is proposed that regulates the underlying states of an unknown linear model through generating informative data and the notion of "regularizability" for a linear system that is of independent interest is introduced.

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme, including a slack variable with regularization in the cost.

Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness

A parametrization of linear feedback systems is derived that paves the way to solve important control problems using data-dependent linear matrix inequalities only and is remarkable in that no explicit system's matrices identification is required.

Finite-Time Adaptive Stabilization of Linear Systems

Using the novel method of random linear feedbacks, high probability guarantees for finite-time stabilization of linear systems with unknown dynamics are established and held for remarkably general settings because of a minimal set of assumptions.

On Controllability and Persistency of Excitation in Data-Driven Control: Extensions of Willems’ Fundamental Lemma

The results shows that data-driven predictive control using online data is equivalent to model predictive control, even for uncontrollable systems, and significantly reduce the amount of data needed in identifying homogeneous multi-agent systems.

Robust data-driven state-feedback design

This work considers the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data, and shows how the proposed framework can be extended to take partial model knowledge into account.

Data-Enabled Predictive Control: In the Shallows of the DeePC

The DeePC algorithm is shown to be equivalent to the classical and widely adopted Model Predictive Control (MPC) algorithm in the case of deterministic linear time-invariant systems and regularizations to the Dee PC algorithm are proposed.

Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator

This work bridges the gap showing that (model free) policy gradient methods globally converge to the optimal solution and are efficient (polynomially so in relevant problem dependent quantities) with regards to their sample and computational complexities.

Learning Sparse Dynamical Systems from a Single Sample Trajectory

A Lasso-like estimator is introduced for the parameters of the LTI system, taking into account their sparse nature, and it is shown that the proposed estimator can correctly identify the sparsity pattern of the system matrices with high probability, provided that the length of the sample trajectory exceeds a threshold.