Simultaneous design of measurement and control strategies for stochastic systems with feedback

doi:10.1016/0005-1098(89)90024-1

Automatica

Volume 25, Issue 5, September 1989, Pages 679-694

https://doi.org/10.1016/0005-1098(89)90024-1 Get rights and content

Abstract

We consider stochastic dynamic decision problems where at each step two consecutive decisions must be taken, one being what information bearing signal(s) to transmit and the other what control action(s) to exert. For finite-horizon problems involving first-order ARMA models with Gaussian statistics and a quadratic cost criterion, we show that the optimal measurement strategy consists of transmitting the innovation linearly at each stage, which in turn leads to optimality of a linear control law. We then extend this result to infinite-horizon models with discounted costs, showing optimality of linear designs. Subsequently, we show that these appealing results do not necessarily carry over to higher order ARMA models, for which we first characterize the best designs within the affine class, and then derive instances of the problem for which there exist non-linear designs that outperform the optimal designs within the affine class. The paper also includes some illustrative numerical examples on the different classes of problems considered.

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Citation Excerpt :
Additionally, if R’s policies are restricted to linear functions, then the proposed approach also computes the optimal signaling rule for arbitrary distributions, since uncorrelatedness yields linear independence. For discrete-time linear Gaussian stochastic systems and in scalar settings, if the measurement signals and the control inputs can be constructed within the class of general policies, and there exists an additive white Gaussian noise (AWGN) channel between the sensor and the controller, reference (Bansal & Başar, 1989) has shown that in the simultaneous (or cooperative) design, the optimal performance in terms of quadratic cost functions can be obtained through linear control inputs, and measurement signals which are linear in the innovation in the state. However, the linear measurement signals may not be optimal for the multidimensional cases in general.
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^☆: The original version of this paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor P. M. Guimarães Ferreira under the direction of Editor H. Kwakernaak.

^‡: Present address: AT&T Bell Laboratories, 6200 E. Broad Street, Columbus, OH 43213, U.S.A.

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PaperSimultaneous design of measurement and control strategies for stochastic systems with feedback☆

Abstract

Automatica

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IEEE Trans. Aut. Control

Simultaneous design of communication strategies and control policies in stochastic systems

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IEEE Trans. Aut. Control

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Paper
Simultaneous design of measurement and control strategies for stochastic systems with feedback☆