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Optimal decentralized statefeedback control with sparsity and delays
, 2015
"... This work presents the solution to a class of decentralized linear quadratic statefeedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into ind ..."
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Cited by 6 (0 self)
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This work presents the solution to a class of decentralized linear quadratic statefeedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into independent subproblems that are solved using dynamic programming. The approach presented herein both unifies and generalizes many existing results.
Structural results and explicit solution for twoplayer LQG systems on a finite time horizon
 In IEEE Conference on Decision and Control, pages 6542 – 6549
, 2013
"... It is wellknown that linear dynamical systems with Gaussian noise and quadratic cost (LQG) satisfy a separation principle. Finding the optimal controller amounts to solving separate dual problems; one for control and one for estimation. For the discretetime finitehorizon case, each problem is a ..."
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Cited by 4 (3 self)
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It is wellknown that linear dynamical systems with Gaussian noise and quadratic cost (LQG) satisfy a separation principle. Finding the optimal controller amounts to solving separate dual problems; one for control and one for estimation. For the discretetime finitehorizon case, each problem is a simple forward or backward recursion. In this paper, we consider a generalization of the LQG problem with two controllers and a partially nested information structure. Each controller is responsible for one of two system inputs, but has access to different subsets of the available measurements. Our paper has three main contributions. First, we prove a fundamental structural result: sufficient statistics for the controllers can be expressed as conditional means of the global state. Second, we give explicit statespace formulae for the optimal controller. These formulae are reminiscent of the classical LQG solution with dual forward and backward recursions, but with the important difference that they are intricately coupled. Lastly, we show how these recursions can be solved efficiently, with computational complexity comparable to that of the centralized problem. 1
Optimal control for LQG systems on graphs—Part I: Structural results. arXiv eprint
, 2014
"... In this twopart paper, we identify a broad class of decentralized outputfeedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among su ..."
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Cited by 1 (1 self)
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In this twopart paper, we identify a broad class of decentralized outputfeedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among subsystems and the intercontroller communication is characterized by the same directed graph. Furthermore, this graph is assumed to be a multitree, that is, its transitive reduction can have at most one directed path connecting each pair of nodes. In this first part, we derive sufficient statistics that may be used to aggregate each controller’s growing available information. Each controller must estimate the states of the subsystems that it affects (its descendants) as well as the subsystems that it observes (its ancestors). The optimal control action for a controller is a linear function of the estimate it computes as well as the estimates computed by all of its ancestors. Moreover, these state estimates may be updated recursively, much like a Kalman filter.
A Separation Principle for Decentralized StateFeedback Optimal Control
"... A cooperative control problem is considered in which dynamically decoupled subsystems must control their own states through state feedback in order to optimize a global quadratic cost. The states of the subsystems are coupled only through the cost function and correlated external disturbances. The ..."
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A cooperative control problem is considered in which dynamically decoupled subsystems must control their own states through state feedback in order to optimize a global quadratic cost. The states of the subsystems are coupled only through the cost function and correlated external disturbances. The architecture is truly decentralized; no communication between subsystems or their controllers is permitted. The main result of this paper is that the optimal decentralized controller satisfies a new separation principle that is strikingly similar to the celebrated result from centralized optimal control theory, but does not appear to follow from it. Roughly speaking, the optimal decentralized control strategy for each subsystem is the product of a static control gain and a global state estimate, and each can be separately computed. 1
Structural results for partially nested LQG systems over graphs
"... We identify a broad class of decentralized outputfeedback LQG systems for which the optimal control strategies have a simple and intuitive estimation structure. We consider cases for which the coupling of dynamics among subsystems and the intercontroller communication are characterized by the s ..."
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We identify a broad class of decentralized outputfeedback LQG systems for which the optimal control strategies have a simple and intuitive estimation structure. We consider cases for which the coupling of dynamics among subsystems and the intercontroller communication are characterized by the same directed graph. For the class of graphs known as multitrees, we show that each controller need only estimate the states of the subsystems it affects (its descendants) as well as the subsystems it observes (its ancestors). The optimal control action for each controller is a linear function of the estimate it computes and the estimates computed by its ancestors. Moreover, all state estimates may be updated recursively, much like a Kalman filter. 1
An Algebraic Approach to the Control of Decentralized Systems
"... Optimal decentralized controller design is notoriously difficult, but recent research has identified large subclasses of such problems that may be convexified and thus are amenable to solution via efficient numerical methods. One recently discovered sufficient condition for convexity is quadratic i ..."
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Optimal decentralized controller design is notoriously difficult, but recent research has identified large subclasses of such problems that may be convexified and thus are amenable to solution via efficient numerical methods. One recently discovered sufficient condition for convexity is quadratic invariance (QI). Despite the simple algebraic characterization of QI, which relates the plant and controller maps, proving convexity of the set of achievable closedloop maps requires tools from functional analysis. In this work, we present a new formulation of quadratic invariance that is purely algebraic. While our results are similar in flavor to those from traditional QI theory, they do not follow from that body of work. Furthermore, they are applicable to new types of systems that are difficult to treat using functional analysis. Examples discussed include rational transfer matrices, systems with delays, and multidimensional systems. I
The H2 control problem for quadratically invariant . . .
"... This paper gives a new solution to the output feedback H2 problem for quadratically invariant communication delay patterns. A characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized H2 problem is cast as a convex model matching problem. The ma ..."
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This paper gives a new solution to the output feedback H2 problem for quadratically invariant communication delay patterns. A characterization of all stabilizing controllers satisfying the delay constraints is given and the decentralized H2 problem is cast as a convex model matching problem. The main result shows that the model matching problem can be reduced to a finitedimensional quadratic program. A recursive statespace method for computing the optimal controller based on vectorization is given.
Optimal control for LQG systems on graphs  Part I: Structural results
, 2014
"... In this twopart paper, we identify a broad class of decentralized outputfeedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among sub ..."
Abstract
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In this twopart paper, we identify a broad class of decentralized outputfeedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among subsystems and the intercontroller communication is characterized by the same directed graph. Furthermore, this graph is assumed to be a multitree, that is, its transitive reduction can have at most one directed path connecting each pair of nodes. In this first part, we derive sufficient statistics that may be used to aggregate each controller’s growing available information. Each controller must estimate the states of the subsystems that it affects (its descendants) as well as the subsystems that it observes (its ancestors). The optimal control action for a controller is a linear function of the estimate it computes as well as the estimates computed by all of its ancestors. Moreover, these state estimates may be updated recursively, much like a Kalman filter.
A Case Study in Network Architecture Tradeoffs *
"... ABSTRACT Software defined networking (SDN) establishes a separation between the control plane and the data plane, allowing network intelligence and state to be centralized in this way the underlying network infrastructure is hidden from the applications. This is in stark contrast to existing distr ..."
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ABSTRACT Software defined networking (SDN) establishes a separation between the control plane and the data plane, allowing network intelligence and state to be centralized in this way the underlying network infrastructure is hidden from the applications. This is in stark contrast to existing distributed networking architectures, in which the control and data planes are vertically combined, and network intelligence and state, as well as applications, are distributed throughout the network. It is also conceivable that some elements of network functionality be implemented in a centralized manner via SDN, and that other components be implemented in a distributed manner. Further, distributed implementations can have varying levels of decentralization, ranging from myopic (in which local algorithms use only local information) to coordinated (in which local algorithms use both local and shared information). In this way, myopic distributed architectures and fully centralized architectures lie at the two extremes of a broader hybrid software defined networking (HySDN) design space. Using admission control as a case study, we leverage recent developments in distributed optimal control to provide network designers with tools to quantitatively compare different architectures, allowing them to explore the relevant HySDN design space in a principled manner. In particular, we assume that routing is done at a slower timescale, and seek to stabilize the network around a desirable operating point despite physical communication delays imposed by the network and rapidly varying traffic demand. We show that there exist scenarios for which one architecture allows for fundamentally better performance than another, thus highlighting the usefulness of the approach proposed in this paper.