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

@article{Talebi2021OnRA,
  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},
  year={2021}
}
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… 

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References

SHOWING 1-10 OF 58 REFERENCES

Online Regulation of Unstable Linear Systems from a Single Trajectory

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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

TLDR
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.
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