Quadratic invariance is necessary and sufficient for convexity

Lessard, Laurent; Lall, Sanjay

doi:10.1109/acc.2011.5990928

Cited by 61 publications

(75 citation statements)

References 6 publications

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“…Quadratic invariance is not only necessary and sufficient for the above equivalence, but also for the linear-fractional transformation of the admissible set to be any convex set [74].…”

Section: Quadratic Invariancementioning

confidence: 99%

Information structures in optimal decentralized control

Mahajan

Martins

Rotkowitz

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

136

153

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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 state-space formulations. The second focus is on norm-optimal control for linear plants under information constraints.

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“…Quadratic invariance is not only necessary and sufficient for the above equivalence, but also for the linear-fractional transformation of the admissible set to be any convex set [74].…”

Section: Quadratic Invariancementioning

confidence: 99%

Information structures in optimal decentralized control

Mahajan

Martins

Rotkowitz

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

136

153

View full text Add to dashboard Cite

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“…More precisely, the set of feasible solutions is often characterized in terms of a property called quadratic invariance, which has been subsequently shown to be necessary and sufficient [20], see also [21] for a review about the recent developments. Nevertheless, these methods always assume that there exists a feasible information pattern, and no restriction is imposed in terms of the sparsity or the cost incurred by a feasible information pattern.…”

Section: Related Workmentioning

confidence: 99%

Minimum cost constrained input-output and control configuration co-design problem: A structural systems approach

Pequito

Kar

Pappas

2015

2015 American Control Conference (ACC)

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In this paper, we study the minimal cost constrained input-output (I/O) and control configuration co-design problem. Given a linear time-invariant plant, where a collection of possible inputs and outputs is known a priori, we aim to determine the collection of inputs, outputs and communication among them incurring in the minimum cost, such that desired control performance, measured in terms of arbitrary poleplacement capability of the closed-loop system, is ensured. We show that this problem is NP-hard in general (in the size of the state space). However, the subclass of problems, in which the dynamic matrix is irreducible, is shown to be polynomially solvable and the corresponding algorithm is presented. In addition, under the same assumption, the same algorithm can be used to solve the minimal cost constrained I/O selection problem, and the minimal cost control configuration selection problem, individually. In order to illustrate the main results of this paper, some simulations are also provided.

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“…• α 1 through α 15 Learning K(s) directly effectively allows the possibility of an arbitrary observer structure and the behavior of additional controller states (e.g., for integral control) to be learned. This parameterization is quite rich, with any linear controller possessing the poles specified with the α i capable of being represented.…”

Section: A Feedback Transfer Functionmentioning

confidence: 99%

“…Witsenhausen's classic counterexample showed that even in the linear-quadratic-gaussian case, the optimal decentralized controller may not be linear, and searching for the optimal linear controller can be a nonconvex problem with many local minima [27]. Recently, very interesting results have emerged describing conditions under which the search for an optimal linear decentralized control is convex in the Youla parameter [22], [15]. An extension to the nonlinear case has also been considered [28].…”

Section: E Decentralized Systemsmentioning

confidence: 99%

Feedback controller parameterizations for Reinforcement Learning

Roberts

Manchester

Tedrake

2011

2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)

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Abstract-Reinforcement Learning offers a very general framework for learning controllers, but its effectiveness is closely tied to the controller parameterization used. Especially when learning feedback controllers for weakly stable systems, ineffective parameterizations can result in unstable controllers and poor performance both in terms of learning convergence and in the cost of the resulting policy. In this paper we explore four linear controller parameterizations in the context of RE-INFORCE, applying them to the control of a reaching task with a linearized flexible manipulator. We find that some natural but naive parameterizations perform very poorly, while the Youla Parameterization (a popular parameterization from the controls literature) offers a number of robustness and performance advantages.

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Quadratic invariance is necessary and sufficient for convexity

Cited by 61 publications

References 6 publications

Information structures in optimal decentralized control

Information structures in optimal decentralized control

Minimum cost constrained input-output and control configuration co-design problem: A structural systems approach

Feedback controller parameterizations for Reinforcement Learning

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