Distributed Learning of Optimal Controls for Linear Systems

Celi, Federico; Baggio, Giacomo; Pasqualetti, Fabio

doi:10.1109/cdc45484.2021.9683707

Cited by 8 publications

(7 citation statements)

References 16 publications

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“…For instance, social networks, power grids, and computer networks are all examples of networked systems. A large literature has dealt with optimal control of networked systems [55], [56], [57], [58], [59], [60], [61], [62], [63].…”

Section: Decoupling Networked Systemsmentioning

confidence: 99%

Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices

Nazerian

Bhatta

Sorrentino

2023

IEEE Open J. Control. Syst.

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In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is 'exact' in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries.

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Section: Decoupling Networked Systemsmentioning

confidence: 99%

Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices

Nazerian

Bhatta

Sorrentino

2023

IEEE Open J. Control. Syst.

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“…where, F 2 and F 4 are as in Lemma 5.2, and U (t − 1) and W (t − 1) are as in (4). Also, we can write Y (t) in ( 4) in terms of U (t − 1), W (t − 1), and V (t):…”

Section: B System Representation In the Behavioral Spacementioning

confidence: 99%

“…where G 1 and G 2 are as in Lemma 5.4, and U (t − 1) and W (t − 1) are as in (4). Using (18), we can substitute x(t − n) in terms of U (t − 1), Y (t), W (t − 1), and V (t) into (23) to get x(t) = Hz(t), where H is as in Lemma 5.4.…”

Section: B System Representation In the Behavioral Spacementioning

confidence: 99%

“…Data-driven control has received increasing interest during the past few years. Specifically, this interest has been surging towards optimal control problems [1]- [4]. The Linear Quadratic Gaussian (LQG) is one of the most fundamental optimal control problems, which deals with partiallyobserved linear dynamical systems in the presence of additive white gaussian noise [5].…”

Section: Introductionmentioning

confidence: 99%

“…In the context of data-driven control, however, the LQG problem is less studied in the literature due to some major challenges: (i) the states of the system cannot be directly measured for learning purposes, (ii) the optimal policy is expressed in the dynamic controller form where it is not unique [5], and (iii) the set of stabilizing controllers can be disconnected [6]. On the other hand, the Linear Quadratic Regulator (LQR) optimal control problem has received more attention in the context of data-driven control [1], [3], [4]. Some of the reasons that make the LQR problem attractive is that the optimal policy can be expressed as a static feedback gain and it is unique [5,Theorem 14.2].…”

Section: Introductionmentioning

confidence: 99%

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Behavioral Feedback for Optimal LQG Control

Makdah

Krishnan

Katewa

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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In this work, we revisit the Linear Quadratic Gaussian (LQG) optimal control problem from a behavioral perspective. Motivated by the suitability of behavioral models for data-driven control, we begin with a reformulation of the LQG problem in the space of input-output behaviors and obtain a complete characterization of the optimal solutions. In particular, we show that the optimal LQG controller can be expressed as a static behavioral-feedback gain, thereby eliminating the need for dynamic state estimation characteristic of state space methods. The static form of the optimal LQG gain also makes it amenable to its computation by gradient descent, which we investigate via numerical experiments. Furthermore, we highlight the advantage of this approach in the data-driven control setting of learning the optimal LQG controller from expert demonstrations. IEEE 61st Conference on Decision and Control (CDC)

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