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

Talebi, Shahriar; Alemzadeh, Siavash; Rahimi, Niyousha; Mesbahi, Mehran

doi:10.1109/tac.2021.3131148

Cited by 10 publications

(12 citation statements)

References 37 publications

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“…However, for general constrained LQR problems, this property does not necessarily hold and gradienct-based methods like Projected Gradient Descent (PGD) are shown with a sub-linear convergence rate to first order stationary points [9]. Recently, the authors of [1] proposed a second order update method for linearly constrained LQR where the Hessian operator is defined based on the Riemannian metric coming from the optimization objective, and the convergence rate was shown to be locally linear-quadratic.…”

Section: Related Workmentioning

confidence: 99%

“…Inspired by this expression, the authors proposed the following covariant 2-tensor field which is shown to be a Riemannian metric and can better capture the geometry property, e.g., the region of positive-definite Hessian is larger [1].…”

Section: Policy Optimization Over Manifold For Static Lq Controlmentioning

confidence: 99%

“…Despite enjoyable performance guarantees, in those existing works of online control ( [3]- [7]), the online controller is typically parameterized as a linear function of the state or past noises, where the coefficient matrices are likely to be dense so that the controller formulation can not satisfy some practical conditions such as the sparsity requirement. For offline LQR problems, the linearly constrained setup was recently studied in [1], where the authors proposed a second order method where the Hessian operator is defined based on a Riemannian metric arising from the optimal control problem itself. In this work, we further extend the idea to the online setup, aiming at providing an adaptive control satisfying the physical constraint in real time.…”

Section: Introductionmentioning

confidence: 99%

“…• Inspired by [1], for linearly constrained online LQG problems, we propose OONM, which is a Riemannian metric based second order approach where the predictions on the cost functions are used during the learning process.…”

Section: Introductionmentioning

confidence: 99%

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On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

Chang

Shahrampour

2021

AAAI

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The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence (V_T) and/or the path-length of the minimizer sequence after T rounds. For strongly convex and smooth functions, Zhang et al. (2017) establish the squared path-length of the minimizer sequence (C*_{2,T}) as a lower bound on regret. They also show that online gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization. We first show that a preconditioned variant of OGD achieves O(min{C*_T,C*_{2,T}}) with one gradient query per round (C*_T refers to the normal path-length). We then propose online optimistic Newton (OON) method for the case when the first and second order information of the function sequence is predictable. The regret bound of OON is captured via the quartic path-length of the minimizer sequence (C*_{4,T}), which can be much smaller than C*_{2,T}. We finally show that by using multiple gradients for OGD, we can achieve an upper bound of O(min{C*_{2,T},V_T}) on regret.

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Section: Related Workmentioning

confidence: 99%

Section: Policy Optimization Over Manifold For Static Lq Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

Chang

Shahrampour

2021

AAAI

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“…The problem of stabilization for unknown linear systems has received considerable attention. Most works have developed methods either under the no-noise (Lamperski, 2020;Talebi et al, 2021b) or stochastic-noise models (Faradonbeh et al, 2018). Many approaches are based on policy gradient and search over a stabilizing feedback gain matrix (Perdomo et al, 2021;Zhao et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Online Adversarial Stabilization of Unknown Networked Systems

Yu¹,

Ho²,

Wierman³

2022

Preprint

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We investigate the problem of stabilizing an unknown networked linear system under communication constraints and adversarial disturbances. We propose the first provably stabilizing algorithm for the problem. The algorithm 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. Our approach avoids the need for system identification and accommodates a broad class of communication delay while being fully distributed and scaling favorably with the number of subsystems in the network.

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Robust data-driven predictive control for unknown linear time-invariant systems

Hu,

Liu

2024

Systems & Control Letters

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

Cited by 10 publications

References 37 publications

On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

Online Adversarial Stabilization of Unknown Networked Systems

Robust data-driven predictive control for unknown linear time-invariant systems

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