On the Exponential Number of Connected Components for the Feasible Set of Optimal Decentralized Control Problems

Han, Feng; Lavaei, Javad

doi:10.23919/acc.2019.8814952

Cited by 34 publications

(50 citation statements)

References 26 publications

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“…The authors proposed a model-free approach and provided a sample complexity analysis. They focused on a finite-horizon setting, since gradient-based optimization methods may not converge to the optimal controller for infinite-horizon decentralized linear quadratic control problems with information constraints, even when the system model is known [17,7]. In [27], the authors proposed a consensus-based model-free learning algorithm for multi-agent decentralized LQR over an infinite horizon, where each agent (i.e., controller) has access to a subset of the global state without delay.…”

Section: Related Workmentioning

confidence: 99%

On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

Ye¹,

Zhu²,

Gupta³

2021

Preprint

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We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a modelbased learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.

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Section: Related Workmentioning

confidence: 99%

On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

Ye¹,

Zhu²,

Gupta³

2021

Preprint

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show abstract

“…Moreover, it is shown that the set of stable SISO systems of order n can not only be non-convex but also disconnected with n + 1 connected components in the Euclidean topology [15]. In fact, for a special class of MIMO systems, one can end up with an exponential number of connected components [7]. 1 We note that the aforementioned results, e.g., [7,15], are for continuous-time systems.…”

mentioning

confidence: 91%

“…In fact, for a special class of MIMO systems, one can end up with an exponential number of connected components [7]. 1 We note that the aforementioned results, e.g., [7,15], are for continuous-time systems.…”

mentioning

confidence: 95%

“…In addition, we discuss properties of the set of structured stabilizing controllers. First, we review the connectedness of the set of stabilizing state-feedback gains for a continuous MIMO system, as recently reported in [7] and discuss their topological and metrical properties: open, contractible and unbounded. In the meantime, the set of stabilizing output-feedback gains is shown to be open, unbounded, and in general, not connected.…”

mentioning

confidence: 99%

“…This is especially the case for the structured case. For example, it was proposed [7] that by employing Schwarz matrices, one may generate an instance where the set of structured Hurwitz stabilizing feedback gains has exponentially many path-connected components. However, as far as we know, there is no counterpart of this phenomena for the set of Schur stable matrices.…”

mentioning

confidence: 99%

See 2 more Smart Citations

On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case

Bu¹,

Mesbahi²,

Mesbahi³

2019

Preprint

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In this paper, we discuss various topological and metrical aspects of the set of stabilizing static feedback gains for multiple-input-multiple-output (MIMO) linear-time-invariant (LTI) systems, in both continuous and discrete-time. Recently, connectivity properties of this set (for continuous time) have been reported in the literature, along with a discussion on how this connectivity is affected by restricting the feedback gain to linear subspaces. We show that analogous to the continuous-time case, one can construct instances where the set of stabilizing feedback gains for discrete time LTI systems has exponentially many connected components.

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On the lack of gradient domination for linear quadratic Gaussian problems with incomplete state information

Mohammadi

Soltanolkotabi

Jovanović

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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On the Exponential Number of Connected Components for the Feasible Set of Optimal Decentralized Control Problems

Cited by 34 publications

References 26 publications

On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case

On the lack of gradient domination for linear quadratic Gaussian problems with incomplete state information

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