Causal coding and control for Markov chains

Varaiya, Pravin; Walrand, Jean

doi:10.1016/0167-6911(83)90012-9

Cited by 30 publications

(15 citation statements)

References 4 publications

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“…and let m 2 be the unique positive root of the standard DARE 2 (mab) 2 p + m(a -1) -b2 = ° q+m (11) Define the control gains kl = kl (R) and k 2 by k . --miab 1 -q+mib2 (12) and steady-state variances ai = ai(R) and a� = a�(R) by a 2 a 2 = (1 -e-2R )kiX, (1 -e-2R )e-2R k w;) , (15) and let ni = N(O,a;) for i = 1,2.…”

Section: Main Results and Some Implicationsmentioning

confidence: 99%

“…(11) and (12), we can show that the second term is equal to the first term, so from (14) Pa 2 1 * (0) � --. (16) …”

Section: I-amentioning

confidence: 92%

“…On the other hand, in the limit R � 00 the Ie-DARE (10) reduces to the usual DARE (11). Hence, ml (00) = m 2 , and both terms on the right-hand side of (14) are equal to m 2 a 2 .…”

Section: -A2mentioning

confidence: 99%

“…These works have offered compelling information theoretic explanations of certain empirically observed fea tures of economic behavior of individuals, firms or institu tions; however, most of them rely on heuristic considerations or on simplifying assumptions pertaining to the structure of observation channels. A parallel line of research on dynamical decision-making with limited information can be found in the control theory literature (a very partial list of references is [11]- [16]). …”

Section: Introductionmentioning

confidence: 99%

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Rational inattention in scalar LQG control

Shafieepoorfard

Raginsky

2013

52nd IEEE Conference on Decision and Control

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Rational Inattention in Scalar LQG Control Ehsan Shafieepoorfard and Maxim RaginskyAhstract-Motivated in part by the "rational inattention" framework of information-constrained decision-making by eco nomic agents, we have recently introduced a general model for average-cost optimal control of Markov processes subject to mutual information constraints [1]. The optimal information constrained control problem reduces to an infinite-dimensional convex program and admits a decomposition based on the Bellman error, which is the object of study in approximate dynamic programming.In this paper, we apply our general theory to an information constrained variant of the scalar linear-quadratic-Gaussian (LQG) control problem. We give an upper bound on the optimal steady-state value of the quadratic performance objective and present explicit constructions of controllers that achieve this bound. We show that the obvious certainty-equivalent control policy is suboptimal when the information constraints are very severe, and exhibit another policy that performs better in this low-information regime. In the two extreme cases of no information (open-loop) and perfect information, these two policies coincide with the optimum.E. Shafieepoorfard and M. Raginsky are with the Department of Electri cal and Computer Engineering and the Coordinated Science Laboratory,

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Section: Main Results and Some Implicationsmentioning

confidence: 99%

“…(11) and (12), we can show that the second term is equal to the first term, so from (14) Pa 2 1 * (0) � --. (16) …”

Section: I-amentioning

confidence: 92%

“…On the other hand, in the limit R � 00 the Ie-DARE (10) reduces to the usual DARE (11). Hence, ml (00) = m 2 , and both terms on the right-hand side of (14) are equal to m 2 a 2 .…”

Section: -A2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rational inattention in scalar LQG control

Shafieepoorfard

Raginsky

2013

52nd IEEE Conference on Decision and Control

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“…On the other hand, dynamic optimization problems where the DM observes the system state through an information-limited channel have been long studied by control theorists (a very partial list of references is [1,3,6,33,34,37,42]). Most of this literature focuses on the case when the channel is fixed, and the controller must be supplemented by a suitable encoder/decoder pair respecting the information constraint and any considerations of causality and delay.…”

mentioning

confidence: 99%

Rationally Inattentive Control of Markov Processes

Shafieepoorfard¹,

Raginsky²,

Meyn³

2016

SIAM J. Control Optim.

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Abstract. The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decisionmaking by economic agents. In the average-cost optimal control framework, the general model introduced in this paper reduces to a variant of the linear-programming representation of the average-cost optimal control problem, subject to an additional mutual information constraint on the randomized stationary policy. The resulting optimization problem is convex and admits a decomposition based on the Bellman error, which is the object of study in approximate dynamic programming. The theory is illustrated through the example of information-constrained linear-quadratic-Gaussian (LQG) control problem. Some results on the infinite-horizon discounted-cost criterion are also presented.

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Causal Coding and Feedback in Gaussian Sensor Networks

Gastpar

Systems and Control: Foundations &Amp; Applications

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Causal coding and control for Markov chains

Cited by 30 publications

References 4 publications

Rational inattention in scalar LQG control

Rational inattention in scalar LQG control

Rationally Inattentive Control of Markov Processes

Causal Coding and Feedback in Gaussian Sensor Networks

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