FeedNetBack - D03.02 - Control Subject to Transmission Constraints, With Transmission Errors

Abstract : This is a Deliverable Report for the FeedNetBack project (www.feednetback.eu). It describes the research performed within Work Package 3, Task 3.2 (Control Subject to Transmission Constraints, with Transmission Errors), in the first 36 months of the project. It targets the issue of control subject to transmission constraints with transmission error. This research concerns problems arising from the presence of a noisy communication channel (specified and modeled at the physical layer) within the control loop. The resulting constraints include finite capacities in the transmission of the sensor and/or actuator signals and transmission errors. Our focus is on designing new compression and coding techniques to support networked control in this scenario. This Deliverable extends the analysis provided in the companion Deliverable D03.01, to deal with the effects of noise in communication channel. The quantization schemes described in D03.01, in particular the adaptive ones, might be very sensitive to the presence of even a few errors. Indeed error-correction coding for estimation or control purposes cannot simply exploit classical coding theory and practice, where vanishing error probability is obtained only in the limit of infinite block-length. A first contribution reported in this Deliverable is the construction of families of codes having the any-time property required in this setting, and the analysis of the trade-off between code complexity and performance. Our results consider the binary erasure channel, and can be extended to more general binary-input output-symmetric memoryless channels. The second and third contributions reported in this deliverable deal with the problem of remotely stabilizing linear time invariant (LTI) systems over Gaussian channels. Specifically, in the second contribution we consider a single LTI system which has to be stabilized by remote controller using a network of sensors having average transmit power constraints. We study basic sensor network topologies and provide necessary and sufficient conditions for mean square stabilization. Then in the third contribution, we extend our study to two LTI systems which are to be simultaneously stabilized. In this regard, we study the interesting setups of joint and separate sensing and control. By joint sensing we mean that there exists a common sensor node to simultaneously transmit the sensed state processes of the two plants and by joint control we mean that there is a common controller for both plants. We name these setups as: i) control over multiple-access channel (separate sensors, joint controller setup), ii) control over broadcast channel (common sensor, separate controllers setup), and iii) control over interference channel (separate sensors, separate controllers). We propose to use delay-free linear schemes for these setups and thus obtain sufficient conditions for mean square stabilization. Then, we discuss the joint design of the encoder and the controller. We propose an iterative design procedure for a joint design of the sensor measurement quantization, channel error protection, and controller actuation, with the objective to minimize the expected linear quadratic cost over a finite horizon. Finally, the same as for the noiseless case, we address the issues that arise when not only one plant and one controller are communicating through a channel, but there is a whole network of sensors and actuators. We consider the effects of digital noisy channels on the consensus algorithm, and we present an algorithm which exploits the any-time codes discussed above.
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Rapport
[Research Report] 2011
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  • HAL Id : hal-00785735, version 1

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Federica Garin, Sandro Zampieri, Lei Bao, Carlos Canudas de Wit, Ruggero Carli, et al.. FeedNetBack - D03.02 - Control Subject to Transmission Constraints, With Transmission Errors. [Research Report] 2011. 〈hal-00785735〉

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