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77
Foundations of control and estimation over lossy networks
 PROCEEDINGS OF THE IEEE
, 2007
"... When data are transmitted to an estimationcontrol 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 estimationcontrol 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 feedbackloop 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. TCPlike 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. UDPlike protocols), the LQG optimal controller is in general nonlinear.
Data Transmission over Networks for Estimation and Control
"... We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology compo ..."
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Cited by 45 (9 self)
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We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal LQG controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network mentioned above. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packetdropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the more commonly used viewpoint of treating a network of communication links as a single endtoend link with the probability of successful transmission determined by some measure of the reliability of the network. I.
Data rate theorem for stabilization over timevarying feedback channels
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2009
"... A data rate theorem for stabilization of a linear, discretetime, dynamical system with arbitrarily large disturbances, over a ratelimited, timevarying communication channel is presented. Necessary and sufficient conditions for stabilization are derived, their implications and relationships with r ..."
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Cited by 41 (5 self)
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A data rate theorem for stabilization of a linear, discretetime, dynamical system with arbitrarily large disturbances, over a ratelimited, timevarying communication channel is presented. Necessary and sufficient conditions for stabilization are derived, their implications and relationships with related results in the literature are discussed. The proof techniques rely on both informationtheoretic and controltheoretic tools.
Optimal control with unreliable communication: the tcp case
 in American Control Conference
, 2005
"... Abstract — The paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimationcontrol unit and between the latter and the actuation points. We consider the case where the arrival of the cont ..."
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Cited by 19 (13 self)
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Abstract — The paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimationcontrol unit and between the latter and the actuation points. We consider the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon our previous results on estimation with unreliable communication, the paper shows the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and and lower bounds on the cost functional. I.
LQG control for distributed systems over TCPlike erasure channels,” DEISUniverity of Calabria
"... Abstract—This paper is concerned with control applications over lossy data network. Sensor data is transmitted to an estimationcontrol unit over a network and control commands are issued to subsystems over the same network. Sensor and control packets may be randomly lost according to a Bernoulli pr ..."
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Cited by 15 (4 self)
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Abstract—This paper is concerned with control applications over lossy data network. Sensor data is transmitted to an estimationcontrol unit over a network and control commands are issued to subsystems over the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this context the discretetime Linear Quadratic Gaussian (LQG) optimal control problem is considered. In [1] a complete analysis was carried out for the case the network is composed of a single sensor and control channel. Here a nontrivial generalization to the case of sensor and actuator networks with p distinct sensor channels and m control channels is presented. It has been proven that the separation principle still holds for all protocols where packets are acknowledged by the receiver (e.g. TCPlike protocols). Moreover it has been pointed out for the first time that the optimal LQG control is a linear function of the state that explicitly depends on the command channels lost probabilities. Such a dependence is not present in preexisting literature, since the amplitude of each control input has to be weighted by the loss probability associated to its own channel. This is not observed in the single channel case. In the infinite horizon case stability conditions on the arrival are derived. Their computation requires the use of Linear Matrix Inequalities (LMIs). I.
Optimizing controller location in networked control systems with packet drops
 IEEE Journal on Selected Areas in Communications
"... Abstract In networked control, there is locational freedom in choosing the node at which to locate the controller, so as to mitigate the effects of packet losses in the network. What is the optimal location for the placement of the control logic? Second, what is the optimal control law in that posi ..."
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Cited by 14 (2 self)
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Abstract In networked control, there is locational freedom in choosing the node at which to locate the controller, so as to mitigate the effects of packet losses in the network. What is the optimal location for the placement of the control logic? Second, what is the optimal control law in that position? The difficulty in answering these two questions is that analysis of optimality in networked control systems subject to random packet drops suffers from Witsenhausen's 'nonclassical information pattern'. Thus, the general problem is considered intractable. We make headway on this problem by using a "Long Packet Assumption", LPA, which allows packets to be arbitrarily long. This is not intended for implementation, but only to develop a lower bound on the cost. In particular, under this assumption the optimal controller location can be shown to be collocated with the actuator. For this position, under the LPA, we can also calculate the optimal cost, which is then a lower bound on the optimal cost for the original problem for all locations. Despite the apparent strength of the LPA, we have found that this lower bound is often close to currently realizable upper bounds. This establishes the near optimality of currently implementable controllers in such instances. Using the lower bound on cost we obtain a necessary condition for stabilizability over all controller locations. This condition matches known sufficient conditions for some special cases, thus establishing a necessary and sufficient condition for location optimized stabilizability of networked control systems with packet loss. * This material is based upon work partially supported by NSF under Contract Nos. ECCS0701604, CCR0325716 and CNS 0519535, USARO under Contract No. DAAD1901010465
LQG control with missing observation and control packets
 in Proceedings of the 16th IFAC World Congress
, 2005
"... Abstract: The paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimationcontrol unit and between the latter and the actuation points. For protocols where packets are acknowledged at the ..."
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Cited by 13 (10 self)
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Abstract: The paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimationcontrol unit and between the latter and the actuation points. For protocols where packets are acknowledged at the receiver (e.g. TCP type protocols), the separation principle holds. Moreover, the optimal LQG control is a linear function of the state. Finally, building upon our previous results on estimation with unreliable communication, the paper shows the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and and lower bounds on the cost functional, and stochastically characterizing their convergence properties in the infinite horizon. More interestingly, it turns out that when there is no feedback on whether a control packet has been delivered or not(e.g. UDP type protocols), the LQG optimal controller is in general nonlinear. A special case when the optimal controller is indeed linear is shown.
On Stability in Presence of Analog Erasure Channels
 Mathematical Theory of Networks and Systems
, 2008
"... Abstract — Consider a discretetime networked control scheme, in which the controller has direct access to noisy measurements of the plant’s output, but the controller and the actuator are connected via a link that features Bernoulli erasure events. We determine necessary and sufficient conditions ..."
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Cited by 13 (3 self)
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Abstract — Consider a discretetime networked control scheme, in which the controller has direct access to noisy measurements of the plant’s output, but the controller and the actuator are connected via a link that features Bernoulli erasure events. We determine necessary and sufficient conditions for the stabilizability of an unstable linear and timeinvariant plant. We show that these conditions are identical for two types of actuators: • (Type I) Processing at the actuator has access to the plant’s model; • (Type II) Processing at the actuator uses a universal algorithm that does not depend on the model of the plant. We also identify cases where availability of acknowledgements over the controlleractuator channel is not required for stability. We also consider decentralized networked control structures, where two or more independent controllerlinkactuator assemblies have access to different measurements of the plant’s output. I.
S.Sastry, “Optimal linear lqg control over lossy networks without packet acknowledgment
 in In Proc. of the 36th Conf. on Decision and Contr
, 2006
"... permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Carnegie Mellon University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotion ..."
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Cited by 12 (5 self)
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permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Carnegie Mellon University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubspermissions@ieee.org.
Sending the Most Recent Observation is not Optimal in Networked Control: Linear Temporal Coding and Towards the Design of a Control Specific Transport Protocol
"... Abstract — This paper explores diversity of temporal observations in a networked control system or sensor network. We analyze what information should be sent between a sensor and a controller (or estimator) in a networked control system (or sensor network) where the two components are separated by a ..."
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Cited by 12 (1 self)
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Abstract — This paper explores diversity of temporal observations in a networked control system or sensor network. We analyze what information should be sent between a sensor and a controller (or estimator) in a networked control system (or sensor network) where the two components are separated by an unreliable, bandwidth limited communication. Packets may be dropped at any time. Given a sensor of limited computational and storage capability restricted to transmitting linear combinations of measurements, we consider what should be transmitted following a packet drop the most recent observation, the previously dropped observation, or a combination of the two? We show that the common practice of sending only the most recent observation is not optimal. We then derive necessary and sufficient conditions for an optimal linear combination of past and present observations. We address a special case where sensor bandwidth (or sampling rate) is higher than communication bandwidth (or throughput), and deal with the case of multiple dropped packets. These results suggest the design of a transport layer specific to networked control which optimizes packet contents contingent on previous packet loss. Alternatively, one could optimize access between contending sensors for a scarce communication medium. The results could be regarded as network coding across time. Simulations are used to illustrate the theoretical results. I.