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133
H2 optimal decentralized control over posets: A state space solution for statefeedback
 in Proceedings of the 49th IEEE Conference on Decision and Control
"... We develop a complete statespace solution to H2optimal decentralized control of posetcausal systems with statefeedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small numb ..."
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Cited by 47 (2 self)
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We develop a complete statespace solution to H2optimal decentralized control of posetcausal systems with statefeedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our statespace characterization of the controller is a remarkable pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to prediction of the state along the different paths on the poset. The results are illustrated by a numerical example. I.
Optimal control of spatially distributed systems
 IEEE Tran. on Automatic Control, September 2006, accepted. [Online]. Available: http://www.grasp.upenn.edu/ ∼ motee/ TACMoteeJ06SD.pdf
"... Abstract — In this paper, we study the structural properties of optimal control of spatially distributed systems. Such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant dependent coupling functions over ar ..."
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Cited by 37 (5 self)
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Abstract — In this paper, we study the structural properties of optimal control of spatially distributed systems. Such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant dependent coupling functions over arbitrary graphs. The key idea of the paper is the introduction of a special class of operators called spatially decaying (SD) operators. We study the structural properties of infinitehorizon linear quadratic optimal controllers for such systems by analyzing the spatial structure of the solution to the corresponding operator Lyapunov and Riccati equations. We prove that the kernel of the optimal feedback of each subsystem decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the system. I.
Design of optimal sparse feedback gains via the alternating direction method of multipliers
 IEEE Trans. Automat. Control
"... Abstract—We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsitypromoting penalty functions into the optim ..."
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Cited by 33 (8 self)
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Abstract—We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsitypromoting penalty functions into the optimal control problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize feedback gains subject to structural constraints determined by the identified sparsity patterns. In the first step, the sparsity structure of feedback gains is identified using the alternating direction method of multipliers, which is a powerful algorithm wellsuited to large optimization problems. This method alternates between promoting the sparsity of the controller and optimizing the closedloop performance, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of the sparsitypromoting penalty functions to decompose the minimization problem into subproblems that can be solved analytically. Several examples are provided to illustrate the effectiveness of the developed approach. Index Terms—Alternating direction method of multipliers (ADMM), communication architectures, continuation methods, minimization, optimization, separable penalty functions, sparsitypromoting optimal control, structured distributed design. I.
Stochastic Nestedness and the Belief Sharing Information Pattern
 IEEE Transactions on Automatic Control
, 2009
"... Abstract—Solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the timehorizon, thus leading to nontractability of classical dynamic programming. A common joint information state supplied to each of the agents leads to a tractable rec ..."
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Cited by 24 (7 self)
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Abstract—Solutions to decentralized stochastic optimization problems lead to recursions in which the state space enlarges with the timehorizon, thus leading to nontractability of classical dynamic programming. A common joint information state supplied to each of the agents leads to a tractable recursion, as is evident in the onestepdelayed information sharing structure case or when deterministic nestedness in information holds when there is a causality relationship as in the case of partially nested information structure. However, communication requirements for such conditions require exchange of very large data noiselessly, hence these assumptions are generally impractical. In this paper, we present a weaker notion of nestedness, which we term as stochastic nestedness, which is characterized by a sequence of Markov chain conditions. It is shown that if the information structure is stochastically nested, then an optimization problem is tractable, and in particular for LQG problems, the team optimal solution is linear, despite the lack of deterministic nestedness or partial nestedness. One other contribution of this paper is that, by regarding the multiple decision makers as a single decision maker and using Witsenhausen’s equivalent model for discretestochastic control, it is shown that the common state required need not consist of observations and it suffices to share beliefs on the state and control actions; a pattern we refer to asstage belief sharing pattern. We discuss the minimum amount of information exchange required to achieve such an information pattern for = 1. The information exchange needed is generally strictly less than what is needed for deterministic nestedness and is zero whenever stochastic nestedness applies. In view of nestedness, we present a discussion on the monotone values of information channels. Index Terms—Communication complexity, decentralized control, informationcontrol structure (ICS), stochastic control, team decision theory. I.
Optimal controller synthesis for a decentralized twoplayer system with partial output feedback
 In American Control Conference
, 2011
"... In this paper, we present a controller synthesis algorithm for a decentralized control problem. We consider an architecture in which there are two interconnected linear subsystems. Both controllers seek to optimize a global quadratic cost, despite having access to different subsets of the available ..."
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Cited by 21 (7 self)
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In this paper, we present a controller synthesis algorithm for a decentralized control problem. We consider an architecture in which there are two interconnected linear subsystems. Both controllers seek to optimize a global quadratic cost, despite having access to different subsets of the available measurements. Many special cases of this problem have previously been solved, most notably the statefeedback case. The generalization to outputfeedback is nontrivial, as the classical separation principle does not hold. Herein, we present the first explicit statespace realization for an optimal controller for the general twoplayer problem. 1
Information Structures in Optimal Decentralized Control
"... Abstract — This tutorial paper provides a comprehensive characterization of information structures in team decision problems and their impact on the tractability of team optimization. Solution methods for team decision problems are presented in various settings where the discussion is structured in ..."
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Cited by 20 (4 self)
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Abstract — This tutorial paper provides a comprehensive characterization of information structures in team decision problems and their impact on the tractability of team optimization. Solution methods for team decision problems are presented in various settings where the discussion is structured in two foci: The first is centered on solution methods for stochastic teams admitting statespace formulations. The second focus is on normoptimal control for linear plants under information constraints. I.
A statespace solution to the twoplayer decentralized optimal control problem
 In Allerton Conference on Communication, Control, and Computing
, 2011
"... In this paper, we present an explicit statespace solution to the twoplayer decentralized optimal control problem. In this problem, there are two interconnected linear systems that seek to optimize a global quadratic cost. Both controllers perform output feedback, but they have access to differen ..."
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Cited by 18 (12 self)
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In this paper, we present an explicit statespace solution to the twoplayer decentralized optimal control problem. In this problem, there are two interconnected linear systems that seek to optimize a global quadratic cost. Both controllers perform output feedback, but they have access to different subsets of the available measurements. The optimal controller, which was not previously known, has a state dimension equal to twice the state dimension of the original system. 1
An explicit statespace solution for a decentralized twoplayer optimal linearquadratic regulator
 In American Control Conference
, 2010
"... We develop controller synthesis algorithms for decentralized control problems, where individual subsystems are connected over a network. We focus on the simplest information structure, consisting of two interconnected linear systems, and construct the optimal controller subject to a decentralizati ..."
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Cited by 18 (3 self)
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We develop controller synthesis algorithms for decentralized control problems, where individual subsystems are connected over a network. We focus on the simplest information structure, consisting of two interconnected linear systems, and construct the optimal controller subject to a decentralization constraint via a spectral factorization approach. We provide explicit statespace formulae for the optimal controller, characterize its order, and show that its states are those of a particular optimal estimator. 1
Decentralized Stochastic Control with Partial History Sharing: A Common Information Approach
, 2012
"... A general model of decentralized stochastic control called partial history sharing information structure is presented. In this model, at each step the controllers share part of their observation and control history with each other. This general model subsumes several existing models of information s ..."
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Cited by 16 (9 self)
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A general model of decentralized stochastic control called partial history sharing information structure is presented. In this model, at each step the controllers share part of their observation and control history with each other. This general model subsumes several existing models of information sharing as special cases. Based on the information commonly known to all the controllers, the decentralized problem is reformulated as an equivalent centralized problem from the perspective of a coordinator. The coordinator knows the common information and select prescriptions that map each controller’s local information to its control actions. The optimal control problem at the coordinator is shown to be a partially observable Markov decision process (POMDP) which is solved using techniques from Markov decision theory. This approach provides (a) structural results for optimal strategies, and (b) a dynamic program for obtaining optimal strategies for all controllers in the original decentralized problem. Thus, this approach unifies the various adhoc approaches taken in the literature. In addition, the structural results on optimal control strategies obtained by the proposed approach cannot be obtained by the existing generic approach (the personbyperson approach) for obtaining structural results in decentralized problems; and the dynamic program obtained by the proposed approach is simpler than that obtained by the existing generic approach (the designer’s approach) for obtaining dynamic programs in decentralized problems.
Sparsitypromoting optimal control for a class of distributed systems
 IN PROCEEDINGS OF THE 2011 AMERICAN CONTROL CONFERENCE
, 2011
"... We consider a linear quadratic optimal control problem with an additional penalty on the number of communication links in the distributed controller. We reformulate this combinatorial optimization problem as a sequence of weighted `1 problems, where the weighted `1 norm approximates the counting o ..."
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Cited by 14 (9 self)
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We consider a linear quadratic optimal control problem with an additional penalty on the number of communication links in the distributed controller. We reformulate this combinatorial optimization problem as a sequence of weighted `1 problems, where the weighted `1 norm approximates the counting of the communication links. We identify a class of systems for which the weighted `1 problem can be formulated as a semidefinite program and therefore its solution can be computed efficiently. Application of the developed algorithm to the optimal control of vehicular formations reveals communication topologies that become sparser as the price of intervehicular communications is increased.