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224
Control under communication constraints
, 2004
"... There is an increasing interest in studying control systems employing multiple sensors and actuators that are geographically distributed. Communication is an important component of these distributed and networked control systems. Hence, there is a need to understand the interactions between the con ..."
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Cited by 350 (9 self)
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There is an increasing interest in studying control systems employing multiple sensors and actuators that are geographically distributed. Communication is an important component of these distributed and networked control systems. Hence, there is a need to understand the interactions between the control components and the communication components of the distributed system. In this paper, we formulate a control problem with a communication channel connecting the sensor to the controller. Our task involves designing the channel encoder and channel decoder along with the controller to achieve different control objectives. We provide upper and lower bounds on the channel rate required to achieve these different control objectives. In many cases, these bounds are tight. In doing so, we characterize the “information complexity” of different control objectives.
A survey of recent results in networked control systems
- PROCEEDINGS OF THE IEEE
, 2007
"... Networked Control Systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. In this paper we review several recent results on estimation, analysis, and controller synthesis for NCSs. The re ..."
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Cited by 300 (11 self)
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Networked Control Systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. In this paper we review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies.
Quantized Feedback Stabilization of Linear Systems
- IEEE Trans. Automat. Control
, 2000
"... This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that ..."
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Cited by 293 (27 self)
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This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear time-invariant feedback, this approach yields global asymptotic stability. Index Terms---Feedback stabilization, hybrid system, linear control system, quantized measurement. I. INTRODUCTION T HIS PAPER deals with quantized feedback stabilization problems for linear time-invariant control systems. A quantizer, as defined here, acts as a functional that maps a real-valued function into a piecewise constant function taking on a finite...
Foundations of control and estimation over lossy networks
- PROCEEDINGS OF THE IEEE
, 2007
"... When data are transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network, both observation and control packets may be lost or delayed. This process can be modeled by assigning probabilities to successfully receive packets. Determini ..."
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Cited by 147 (26 self)
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When data are transmitted to an estimation-control unit over a network, and control commands are issued to subsystems over the same network, both observation and control packets may be lost or delayed. This process can be modeled by assigning probabilities to successfully receive packets. Determining the impact of this uncertainty on the feedback-loop requires a generalization of classical control theory. This paper presents the foundations of such new theory. Motivations and overview of the efforts of different research groups are described first. Then, novel contributions of the authors are presented. These include showing threshold behaviors which are governed by the uncertainty parameters of the communication network: for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g. TCP-like protocols), there exists critical probabilities for the successful delivery of packets, below which the optimal controller fails to stabilize the system. Furthermore, for these protocols, the separation principle holds and the optimal LQG control is a linear function of the estimated state. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g. UDP-like protocols), the LQG optimal controller is in general nonlinear.
Stabilizability of stochastic linear systems with finite feedback data rates
- SIAM JOUR. CONTR. OPTIM
, 2004
"... Feedback control with limited data rates is an emerging area which incorporates ideas from both control and information theory. A fundamental question it poses is how low the closed loop data rate can be made before a given dynamical system is impossible to stabilize by any coding and control law. ..."
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Cited by 136 (8 self)
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Feedback control with limited data rates is an emerging area which incorporates ideas from both control and information theory. A fundamental question it poses is how low the closed loop data rate can be made before a given dynamical system is impossible to stabilize by any coding and control law. Analagously to source coding, this defines the smallest error-free data rate sufficient to achieve “reliable ” control, and explicit expressions for it have been derived for linear timeinvariant systems without disturbances. In this paper, the more general case of finite-dimensional linear systems with process and observation noise is considered, the object being mean square state stability. By inductive arguments employing the entropy power inequality of information theory, and a new quantizer error bound, an explicit expression for the infimum stabilizing data rate is derived, under very mild conditions on the initial state and noise probability distributions.
Stochastic Linear Control over a Communication Channel
, 2003
"... We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular we examine the role communic ..."
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Cited by 85 (9 self)
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We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular we examine the role communication has on the classical LQG problem. We give conditions under which the classical separation property between estimation and control holds and the certainty equivalent control law is optimal. We then present the sequential rate distortion framework. We present bounds on the achievable performance and show the inherent tradeo#s between control and communication costs. In particular we show that optimal quadratic cost decomposes into two terms: a full knowledge cost and a sequential rate distortion cost.
Towards the control of linear systems with minimum bit-rate
- In Proc. of the Int. Symp. on the Mathematical Theory of Networks and Syst
, 2002
"... We address the problem of determining the minimum bit-rate needed to stabilize a linear time-invariant process. For the noise free case, we determine a bit-rate below which stabilization is not possible and above which asymptotic stabilization can be achieved. Inspired by differential pulse code mod ..."
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Cited by 73 (14 self)
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We address the problem of determining the minimum bit-rate needed to stabilize a linear time-invariant process. For the noise free case, we determine a bit-rate below which stabilization is not possible and above which asymptotic stabilization can be achieved. Inspired by differential pulse code modulation (DPCM) techniques, we propose practical encoding/decoding schemes that guarantee boundedness of the state for the case of a noisy linear time-invariant process. With fixed-step quantization, we are only able to approach the minimum bit-rate for the noiseless case. However, with variable-step quantization we are able to approach it even in the presence of noise and disturbances. 1
Stabilization of nonlinear systems with limited information feedback
- IEEE Trans. Automat. Control
, 2005
"... Abstract—This note is concerned with the problem of stabilizing a nonlinear continuous-time system by using sampled encoded measurements of the state. We demonstrate that global asymptotic stabilization is possible if a suitable relationship holds between the number of values taken by the encoder, t ..."
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Cited by 69 (10 self)
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Abstract—This note is concerned with the problem of stabilizing a nonlinear continuous-time system by using sampled encoded measurements of the state. We demonstrate that global asymptotic stabilization is possible if a suitable relationship holds between the number of values taken by the encoder, the sampling period, and a system parameter, provided that a feedback law achieving input-to-state stability with respect to measurement errors can be found. The issue of relaxing the latter condition is also discussed. Index Terms—Asymptotic stability, encoding, input-to-state stability, limited information, measurement errors, nonlinear system.
Topological feedback entropy and nonlinear stabilization
- IEEE Transactions on Automatic Control
, 2004
"... Abstract—It is well known in the field of dynamical systems that entropy can be defined rigorously for completely deterministic open-loop systems. However, such definitions have found limited application in engineering, unlike Shannon’s statistical entropy. In this paper, it is shown that the proble ..."
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Cited by 57 (5 self)
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Abstract—It is well known in the field of dynamical systems that entropy can be defined rigorously for completely deterministic open-loop systems. However, such definitions have found limited application in engineering, unlike Shannon’s statistical entropy. In this paper, it is shown that the problem of communication-lim-ited stabilization is related to the concept of topological entropy, introduced by Adler et al. as a measure of the information rate of a continuous map on a compact topological space. Using similar open cover techniques, the notion of topological feedback entropy (TFE) is defined in this paper and proposed as a measure of the inherent rate at which a map on a noncompact topological space with inputs generates stability information. It is then proven that a topological dynamical plant can be stabilized into a compact set if and only if the data rate in the feedback loop exceeds the TFE of the plant on the set. By taking appropriate limits in a metric space, the concept of local TFE (LTFE) is defined at fixed points of the plant, and it is shown that the plant is locally uniformly asymptotically stabilizable to a fixed point if and only if the data rate exceeds the plant LTFE at the fixed point. For continuously differentiable plants in Euclidean space, real Jordan forms and volume partitioning arguments are then used to derive an expres-sion for LTFE in terms of the unstable eigenvalues of the fixed point Jacobian. Index Terms—Communication channels, stabilizability, topolog-ical entropy.
Event-triggering in distributed networked control systems
"... Abstract—This paper examines event-triggered data transmis-sion in distributed networked control systems with packet loss and transmission delays. We propose a distributed event-triggering scheme, where a subsystem broadcasts its state information to its neighbors only when the subsystem’s local sta ..."
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Cited by 57 (7 self)
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Abstract—This paper examines event-triggered data transmis-sion in distributed networked control systems with packet loss and transmission delays. We propose a distributed event-triggering scheme, where a subsystem broadcasts its state information to its neighbors only when the subsystem’s local state error exceeds a specified threshold. In this scheme, a subsystem is able to make broadcast decisions using its locally sampled data. It can also locally predict the maximal allowable number of successive data dropouts (MANSD) and the state-based deadlines for transmission delays. Moreover, the designer’s selection of the local event for a subsystem only requires information on that individual subsystem. Our analysis applies to both linear and nonlinear subsystems. Designing local events for a nonlinear subsystem requires us to find a controller that ensures that subsystem to be input-to-state stable. For linear subsystems, the design problem becomes a linear matrix inequality feasibility problem. With the assumption that the number of each subsystem’s successive data dropouts is less than its MANSD, we show that if the transmission delays are zero, the resulting system is finite-gain stable. If the delays are bounded by given deadlines, the system is asymptotically stable. We also show that those state-based deadlines for transmission delays are always greater than a positive constant. Index Terms—Distributed systems, event-triggering, networked control systems (NCS). I.
