Stabilizing Error Correction Codes for Controlling LTI Systems over Erasure Channels

We propose (k,k') stabilizing codes, which is a type of delayless error correction codes that are useful for control over networks with erasures. For each input symbol, k output symbols are generated by the stabilizing code. Receiving any k' of these outputs guarantees stability. Thus, the system to be stabilized is taken into account in the design of the erasure codes. Our focus is on LTI systems, and we construct codes based on independent encodings and multiple descriptions. The theoretical efficiency and performance of the codes are assessed, and their practical performances are demonstrated in a simulation study. There is a significant gain over other delayless codes such as repetition codes.Comment: Accepted and presented at the IEEE 60th Conference on Decision and Control (CDC). arXiv admin note: substantial text overlap with arXiv:2112.1171

Stabilization of Linear Systems Over Gaussian Networks

The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes operate subject to an average transmit power constraint and they can cooperate to communicate the observations of the plant's state to the remote controller. The communication links between all nodes are modeled as Gaussian channels. Necessary as well as sufficient conditions for mean-square stabilization over various network topologies are derived. The sufficient conditions are in general obtained using delay-free linear policies and the necessary conditions are obtained using information theoretic tools. Different settings where linear policies are optimal, asymptotically optimal (in certain parameters of the system) and suboptimal have been identified. For the case with noisy multi-dimensional sources controlled over scalar channels, it is shown that linear time varying policies lead to minimum capacity requirements, meeting the fundamental lower bound. For the case with noiseless sources and parallel channels, non-linear policies which meet the lower bound have been identified

Kalman Filtering With Relays Over Wireless Fading Channels

This note studies the use of relays to improve the performance of Kalman filtering over packet dropping links. Packet reception probabilities are governed by time-varying fading channel gains, and the sensor and relay transmit powers. We consider situations with multiple sensors and relays, where each relay can either forward one of the sensors' measurements to the gateway/fusion center, or perform a simple linear network coding operation on some of the sensor measurements. Using an expected error covariance performance measure, we consider optimal and suboptimal methods for finding the best relay configuration, and power control problems for optimizing the Kalman filter performance. Our methods show that significant performance gains can be obtained through the use of relays, network coding and power control, with at least 30-40$\%$ less power consumption for a given expected error covariance specification.Comment: 7 page

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

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

Minimum-Information LQG Control - Part I: Memoryless Controllers

With the increased demand for power efficiency in feedback-control systems, communication is becoming a limiting factor, raising the need to trade off the external cost that they incur with the capacity of the controller's communication channels. With a proper design of the channels, this translates into a sequential rate-distortion problem, where we minimize the rate of information required for the controller's operation under a constraint on its external cost. Memoryless controllers are of particular interest both for the simplicity and frugality of their implementation and as a basis for studying more complex controllers. In this paper we present the optimality principle for memoryless linear controllers that utilize minimal information rates to achieve a guaranteed external-cost level. We also study the interesting and useful phenomenology of the optimal controller, such as the principled reduction of its order

On Kalman Filtering over Fading Wireless Channels with Controlled Transmission Powers

We study stochastic stability of centralized Kalman filtering for linear time-varying systems equipped with wireless sensors. Transmission is over fading channels where variable channel gains are counteracted by power control to alleviate the effects of packet drops. We establish sufficient conditions for the expected value of the Kalman filter covariance matrix to be exponentially bounded in norm. The conditions obtained are then used to formulate stabilizing power control policies which minimize the total sensor power budget. In deriving the optimal power control laws, both statistical channel information and full channel information are considered. The effect of system instability on the power budget is also investigated for both these cases

Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control

The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control