Optimal decentralized state-feedback control with sparsity and delays

This paper studies convex stochastic dynamic team problems with finite and infinite time horizons under decentralized information structures. First, we introduce two notions called exchangeable teams and symmetric information structures. We show that in convex exchangeable team problems an optimal policy exhibits a symmetry structure. We give a characterization for such symmetrically optimal teams for a general class of convex dynamic team problems under mild conditional independence conditions. In addition, through concentration of measure arguments, we establish the convergence of optimal policies for teams with N decision makers to the corresponding optimal policies for symmetric mean-field teams with infinitely many decision makers. As a by-product, we present an existence result for convex mean-field teams, where the main contribution of our paper is with respect to the information structure in the system when compared with the related results in the literature that have either assumed a classical information structure or a static information structure. We also apply these results to the important special case of LQG team problems, where while for partially nested LQG team problems with finite time horizons it is known that the optimal policies are linear, for infinite horizon problems the linearity of optimal policies has not been established in full generality. We also study average cost finite and infinite horizon dynamic team problems with a symmetric partially nested information structure and obtain globally optimal solutions where we establish linearity of optimal policies. Moreover, we also study average cost infinite horizon LQG dynamic teams under sparsity and delay constraints.

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“…where (X s t+1 ) {i},{i} denotes the sub-matrix (X s t+1 ) corresponds to the ii-th array. In the following, we refine a related result in [24].…”

Section: 2supporting

confidence: 70%

Convex Symmetric Stochastic Dynamic Teams and Their Mean-Field Limit

Sanjari

Yüksel

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…DECOMPOSITION In this section we proceed to define the dual problem to (22), which allows to transform the original constrained problem (8) into an unconstrained one. To this end, we introduce dual variables S(k) ∈ R n×n , k = 0, .…”

Section: Information-oriented Optimization Via Dualmentioning

confidence: 99%

“…i. The problem (8) is decoupled into the sum of independent sub-problems that are linear in the respective decision variables, i.e., it is equivalent to…”

Section: B Optimal Information-constrained Controlmentioning

confidence: 99%

Information-Constrained Optimal Control of Distributed Systems with Power Constraints

Causevic

Abara

Hirche

2018

2018 European Control Conference (ECC)

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In this paper we address the problem of information-constrained optimal control for an interconnected system subject to one-step communication delays and power constraints. The goal is to minimize a finite-horizon quadratic cost by optimally choosing the control inputs for the subsystems, accounting for power constraints in the overall system and different information available at the decision makers. To this purpose, due to the quadratic nature of the power constraints, the LQG problem is reformulated as a linear problem in the covariance of state-input aggregated vector. The zeroduality gap allows us to equivalently consider the dual problem, and decompose it into several sub-problems according to the information structure present in the system. Finally, the optimal control inputs are found in a form that allows for offline computation of the control gains.

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“…All these approaches are formulated in the frequency domain and solve the infinite horizon problem of constructing a stabilizing feedback controller that minimizes the H 2 /H ∞ norm of the closed loop system. In very recent work [LL13], the authors show that for decentralization constraints arising from certain nested information structures, the feedback synthesis problem can be solved using dynamic programming techniques directly in state-space form.…”

Section: Introductionmentioning

confidence: 99%

Convexity of optimal linear controller design

Dvijotham

Theodorou

Todorov

et al. 2013

52nd IEEE Conference on Decision and Control

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Abstract-We develop a general class of stochastic optimal control problems for which the problem of designing optimal linear feedback gains is convex. The class of problems includes arbitrary time varying linear systems and costs that are mixtures of exponentiated quadratics. This allows us to model problems with quadratic state costs and linear constraints on states and state transitions. Further, convexity in the feedback gains lets us impose arbitrary convex constraints or penalties on the feedback matrix: Thus we can model problems like distributed control (by imposing a sparsity structure on the feedback matrix) and variable-stiffness control (by applying time-varying penalties to feedback gain matrices). We show that the convex optimization problem can be solved efficiently by using the structure of the matrices involved. Finally, we present an application of these ideas to a practical problem arising in distributed control of power systems.

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Optimal decentralized state-feedback control with sparsity and delays

Cited by 69 publications

References 34 publications

Convex Symmetric Stochastic Dynamic Teams and Their Mean-Field Limit

Convex Symmetric Stochastic Dynamic Teams and Their Mean-Field Limit

Information-Constrained Optimal Control of Distributed Systems with Power Constraints

Convexity of optimal linear controller design

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