We consider a joint sensor and controller design problem for linear Gaussian stochastic systems in which a weighted sum of quadratic control cost and the amount of information acquired by the sensor is minimized. This problem formulation is motivated by situations where a control law must be designed in the presence of sensing, communication, and privacy constraints. We show that the optimal joint sensor-controller design is relatively easy when the sensing policy is restricted to be linear. Namely, an explicit form of the optimal linear sensor equation, the Kalman filter, and the certainty equivalence controller that jointly solves the problem can be efficiently found by semidefinite programming (SDP). Whether the linearity assumption in our design is restrictive or not is currently an open problem.
Feedback control over noisy channels has been a popular research topic in the past two decades. Most of the early contributions focus on stabilization of unstable dynamical systems using feeback control over band-limited communication channels. A very partial list of papers in this context is @cite_16 @cite_5 @cite_8 @cite_12 @cite_21 @cite_14 @cite_2 . This research direction naturally leads to trade-off studies between the achievable control performance and the required capacity of the sensor-controller communication channel. If the communication rate is finite, larger block length (achieving high resolution) is not necessarily preferred since the resulting delay leads to the loss of control performance @cite_24 . LQG control performance subject to capacity constraints is considered in @cite_23 , where a certain separation principle" between control design and communication design is reported. The authors of @cite_11 consider a fundamental performance limitation of the finite horizon minimum-variance control (MVC) over noisy communication channels in the LQG regime. More comprehensive literature surveys on control designs over communication channels are available in @cite_19 @cite_25 @cite_7 @cite_22 .
@cite_14 @cite_22 @cite_7 @cite_8 @cite_21 @cite_24 @cite_19 @cite_23 @cite_2 @cite_5 @cite_16 @cite_25 @cite_12 @cite_11
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Consider a control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We study the fundamental tradeoff between the communication rate @math bits sec and the expected cost @math . We obtain a lower bound on a certain rate-cost function, which quantifies the minimum directed mutual information between the channel input and output that is compatible with a target LQR cost. The rate-cost function has operational significance in multiple scenarios of interest: among others, it allows us to lower-bound the minimum communication rate for fixed and variable length quantization, and for control over noisy channels. We derive an explicit lower bound to the rate-cost function, which applies to the vector, non-Gaussian, and partially observed systems, thereby extending and generalizing an earlier explicit expression for the scalar Gaussian system, due to Tatikonda el al. The bound applies as long as the system noise has a probability density function. It can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state. Via a separation principle between control and communication, similar results hold for causal lossy compression of additive noise Markov sources. Apart from standard dynamic programming arguments, our technical approach leverages the Shannon lower bound, develops new estimates for data compression with coding memory, and uses some recent results on high resolution variable-length vector quantization to prove that the new converse bounds are tight. In this paper, we consider a robust network control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller and the controller and plant. We investigate the effect of data drop out in the form of packet losses. Four distinct control schemes are explored and sufficient conditions to ensure almost sure stability of the closed loop system are derived for each of them in terms of minimum packet arrival rate and the maximum uncertainty. I. INTRODUCTION In the past decade, networked control systems (NCS) have gained much attention from both the control com- munity and the network and communication community. When compared with classical feedback control system, networked control systems have several advantages. For example, they can reduce the system wiring, make the system easy to operate and maintain and later diagnose in case of malfunctioning, and increase system agility (20). Although NCS have advantages, inserting a network in between the plant and the controller introduces many problems as well. For instance, zero-delayed sensing and actuation, perfect information and synchronization are no longer guaranteed in the new system architecture as only finite bandwidth is available and data packet drops and delays may occur due to network traffic conditions. These must be revisited and analyzed before networked control systems become prevalent. Recently, many researchers have spent effort on these issues and some significant results were obtained and many are in progress. Many of the aforementioned issues are studied separately. Tatikonda (19) and Sahai (13) have presented some interesting results in the area of control under communication constraints. Specifically, Tatikonda gave a necessary and sufficient condition on the channel data rate such that a noiseless LTI system in the closed loop is asymptotically stable. He also gave rate results for stabilizing a noisy LTI system over a digital channel. Sahai proposed the notion of anytime capacity to deal with real time estimation and control for a networked control system. In our paper (17), the authors have considered various rate issues under finite bandwidth, packet drops and finite controls. An optimal bit allocation scheme is given in (16) under the networked setting. The effect of pacekt drops on state estimation was studied by Sinopoli, et. al. in (3). It has further been investigated by many researchers including the present authors in (15) and (6). Abstract The paper considers the problem of robust stabilization of linear uncertain discrete-time systems via limited capacity communication channels. We consider the case when the control input is to be transmitted via communication channel with a bit-rate constraint. A constructive method to design a robustly stabilizing controller is proposed. Wireless vehicle-to-vehicle (V2V) and vehicle-toinfrastructure (V2I) communication holds great promise for significantly reducing the human and financial costs of vehicle collisions. A common characteristic of this communication is the broadcast of a device's core state information at regular intervals (e.g., vehicle speed and location or traffic signal state and timing). Unless controlled, the aggregate of these broadcasts will congest the channel under dense traffic scenarios, reducing the effectiveness of collision avoidance applications that use transmitted information. Active congestion control using distributed techniques is a topic of great interest for establishing the scalability of this technology. This paper defines a new adaptive congestion control algorithm that can be applied to the message rate of devices in this vehicular environment. While other published approaches rely on binary control, the LInear MEssage Rate Integrated Control (LIMERIC) algorithm takes advantage of full-precision control inputs that are available on the wireless channel. The result is provable convergence to fair and efficient channel utilization in the deterministic environment, under simple criteria for setting adaptive parameters. This “perfect” convergence avoids the limit cycle behavior that is inherent to binary control. We also discuss several practical aspects associated with implementing LIMERIC, including guidelines for the choice of system parameters to obtain desired utilization outcomes, a gain saturation technique that maintains robust convergence under all conditions, convergence with asynchronous updates, and using channel load to determine the aggregate message rate that is observable at a receiver. This paper also extends the convergence analysis for two important cases, i.e., measurement noise in the input signal and delay in the update process. This paper illustrates key analytical results using MATLAB numerical results and employs standard NS-2 simulations to demonstrate the performance of LIMERIC in several high-density scenarios. In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-Lambda channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper. For output-symmetric discrete memoryless channels (DMCs) at even moderately high rates, fixed-block-length communication systems show no improvements in their error exponents with feedback. This paper studies systems with fixed end-to-end delay and shows that feedback generally provides dramatic gains in the error exponents. A new upper bound (the uncertainty-focusing bound) is given on the probability of symbol error in a fixed-delay communication system with feedback. This bound turns out to have a form similar to Viterbi's bound used for the block error probability of convolutional codes as a function of the fixed constraint length. The uncertainty-focusing bound is shown to be asymptotically achievable with noiseless feedback for erasure channels as well as for any output-symmetric DMC that has strictly positive zero-error capacity. Furthermore, it can be achieved in a delay-universal (anytime) fashion even if the feedback itself is delayed by a small amount. Finally, it is shown that for end-to-end delay, it is generally possible at high rates to beat the sphere-packing bound for general DMCs - thereby providing a counterexample to a conjecture of Pinsker. In this paper, we study resource allocation for a multicarrier-based cognitive radio (CR) network. More specifically, we investigate the problem of secondary users’ energy-efficiency (EE) maximization problem under secondary total power and primary interference constraints. First, assuming cooperation among the secondary base stations (BSs), a centralized approach is considered to solve the EE optimization problem for the CR network where the primary and secondary users are using either orthogonal frequency-division multiplexing (OFDM) or filter bank based multicarrier (FBMC) modulations. We propose an alternating-based approach to solve the joint power-subcarrier allocation problem. More importantly, in the first place, subcarriers are allocated using a heuristic method for a given feasible power allocation. Then, we conservatively approximate the nonconvex power control problem and propose a joint successive convex approximation-Dinkelbach algorithm (SCADA) to efficiently obtain a solution to the nonconvex power control problem. The proposed algorithm is shown to converge to a solution that coincides with the stationary point of the original nonconvex power control subproblem. Moreover, we propose a dual decomposition-based decentralized version of the SCADA. Second, under the assumption of no cooperation among the secondary BSs, we propose a fully distributed power control algorithm from the perspective of game theory. The proposed algorithm is shown to converge to a Nash-equilibrium (NE) point. Moreover, we propose a sufficient condition that guarantees the uniqueness of the achieved NE. Extensive simulation analyses are further provided to highlight the advantages and demonstrate the efficiency of our proposed schemes. In this paper, we consider two different models of partial channel state information at the base station transmitter (CSIT) for multiple antenna broadcast channels: 1) the shape feedback model where the normalized channel vector of each user is available at the base station and 2) the limited feedback model where each user quantizes its channel vector according to a rotated codebook that is optimal in the sense of mean squared error and feeds back the codeword index. This paper is focused on characterizing the sum rate performance of both zero-forcing dirty paper coding (ZFDPC) systems and channel inversion (CI) systems under the given two partial CSIT models. Intuitively speaking, a system with shape feedback loses the sum rate gain of adaptive power allocation. However, shape feedback still provides enough channel knowledge for ZFDPC and CI to approach their own optimal throughput in the high signal-to-noise ratio (SNR) regime. As for limited feedback, we derive sum rate bounds for both signaling schemes and link their throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for both schemes for asymptotically high SNR. In this paper, we introduce a fundamental principle for optimal communication over general memoryless channels in the presence of noiseless feedback, termed posterior matching. Using this principle, we devise a (simple, sequential) generic feedback transmission scheme suitable for a large class of memoryless channels and input distributions, achieving any rate below the corresponding mutual information. This provides a unified framework for optimal feedback communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath scheme (AWGN channel) are special cases. Thus, as a corollary, we prove that the Horstein scheme indeed attains the BSC capacity, settling a longstanding conjecture. We further provide closed form expressions for the error probability of the scheme over a range of rates, and derive the achievable rates in a mismatch setting where the scheme is designed according to the wrong channel model. Several illustrative examples of the posterior matching scheme for specific channels are given, and the corresponding error probability expressions are evaluated. The proof techniques employed utilize novel relations between information rates and contraction properties of iterated function systems. In this paper, we review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, another sense of capacity (parametrized by reliability) called "anytime capacity" is necessary for the stabilization of an unstable process. The required rate is given by the log of the unstable system gain and the required reliability comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk-Kailath scheme for communication over the additive white Gaussian noise (AWGN) channel with feedback. In cases of sufficiently rich information patterns between the encoder and decoder, adequate anytime capacity is also shown to be sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations, delayed control actions, and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to continuous time systems as well. We close with comments discussing a hierarchy of difficulty for communication problems and how these results establish where stabilization problems sit in that hierarchy Several works have established links between congestion control in communication networks and feedback control theory. In this paper, following this paradigm, the design of an AQM (active queue management) ensuring the stability of the congestion phenomenon at a router is proposed. To this end, a modified fluid flow model of TCP (transmission control protocol) that takes into account all delays of the topology is introduced. Then, appropriate tools from control theory are used to address the stability issue and to cope with the time-varying nature of the multiple delays. More precisely, the design of the AQM is formulated as a structured state feedback for multiple time delay systems through the quadratic separation framework. The objective of this mechanism is to ensure the regulation of the queue size of the congested router as well as flow rates to a prescribed level. Furthermore, the proposed methodology allows to set arbitrarily the QoS (quality of service) of the communications following through the controlled router. Finally, a numerical example and some simulations support the exposed theory. In this paper, the problem of feedback and active user selection in multiple-input single-output (MISO) wireless systems such that the system’s stability region is as big as possible is examined. The focus is on a system in a Rayleigh fading environment where zero forcing precoding is used to serve all active users in every slot. Acquisition of the channel states is done via uplink training in time division duplexing mode by the active users. Clearly, only a subset of users can perform uplink training and the selection of this subset is a challenging and interesting problem especially in MISO systems. The stability regions of a baseline centralized scheme and two novel decentralized policies are examined analytically. In the decentralized schemes, the transmitter broadcasts periodically the queue state information and the users contend for the channel in a carrier sense multiple access-based manner with parameters based on the outdated queue state information and real-time channel state information. We show that, using infrequent signaling between the base station and the users, the decentralized policies outperform the centralized policy. In addition, a threshold-based user selection and training scheme for discrete-time contention is proposed. The results of this paper imply that, as far as stability is concerned, the users must be involved in the active user selection and feedback training decision. This should be leveraged in future communication systems. Most cellular radio systems provide for the use of transmitter power control to reduce cochannel interference for a given channel allocation. Efficient interference management aims at achieving acceptable carrier-to-interference ratios in all active communication links in the system. Such schemes for the control of cochannel interference are investigated. The effect of adjacent channel interference is neglected. As a performance measure, the interference (outage) probability is used, i.e., the probability that a randomly chosen link is subject to excessive interference. In order to derive upper performance bounds for transmitter power control schemes, algorithms that are optimum in the sense that the interference probability is minimized are suggested. Numerical results indicate that these upper bounds exceed the performance of conventional systems by an order of magnitude regarding interference suppression and by a factor of 3 to 4 regarding the system capacity. The structure of the optimum algorithm shows that efficient power control and dynamic channel assignment algorithms are closely related. > For a memoryless channel, although feedback cannot increase capacity, it can reduce the complexity and or improve the error performance of a communication system. Recently, Shayevitz and Feder proposed the posterior matching scheme (PMS) which is a simple recursive transmission scheme that achieves the capacity of memoryless channels with feedback. Furthermore, Coleman provided a Lyapunov function approach to prove capacity achievability of the PMS. In this paper, we investigate a capacity-achieving PMS for the case of finite-state channels (FSCs). We first derive a single-letter expression for the capacity of the FSC with delayed output and state feedback by formulating the problem in a stochastic control framework. The resulting capacity expression can be evaluated using dynamic programming. We then propose a simple recursive PMS-like transmission scheme. To prove capacity achievability of the proposed PMS, we identify an appropriate Markov chain induced by the PMS. 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. Analogously 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 time-invariant 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. In some communication problems, it is a good assumption that the channel consists of an additive white Gaussian noise forward link and an essentially noiseless feedback link. In this paper, we study channels where no bandwidth constraint is placed on the transmitted signals. Such channels arise in space communications. It is known that the availability of the feedback link cannot increase the channel capacity of the noisy forward link, but it can considerably reduce the coding effort required to achieve a given level of performance. We present a coding scheme that exploits the feedback to achieve considerable reductions in coding and decoding complexity and delay over what would be needed for comparable performance with the best known (simplex) codes for the one-way channel. Our scheme, which was motivated by the Robbins-Monro stochastic approximation technique, can also be used over channels where the additive noise is not Gaussian but is still independent from instant to instant. An extension of the scheme for channels with limited signal bandwidth is presented in a companion paper (Part II). We consider QoS-aware spectrum sharing in cognitive wireless networks where secondary users are allowed to access the spectrum owned by a primary network provider. The interference from secondary users to primary users is constrained to be below the tolerable limit. Also, signal to interference plus noise ratio (SINR) of each secondary user is maintained higher than a desired level for QoS insurance. When network load is high, admission control needs to be performed to satisfy both QoS and interference constraints. We propose an admission control algorithm which is performed jointly with power control such that QoS requirements of all admitted secondary users are satisfied while keeping the interference to primary users below the tolerable limit. When all secondary users can be supported at minimum rates, we allow them to increase their transmission rates and share the spectrum in a fair manner. We formulate the joint power rate allocation with max-min fairness criterion as an optimization problem. We show how to transform it into a convex optimization problem so that its globally optimal solution can be obtained. Numerical results show that the proposed admission control algorithm achieves performance very close to the optimal solution. Also, impacts of different system and QoS parameters on the network performance are investigated for both admission control and rate power allocation problems. In this paper, the fundamental performance tradeoff of the delay-limited multiple-input multiple-output (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity-multiplexing tradeoff investigated by Zheng and Tse in standard delay-limited MIMO channels with coherent detection to the ARQ scenario. We establish the three-dimensional tradeoff between reliability (i.e., diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain. Interestingly, ARQ diversity appears even in long-term static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be used to dramatically increase the diversity advantage. Our analysis reveals some important insights on the benefits of ARQ in slow-fading MIMO channels. In particular, we show that 1) allowing for a sufficiently large retransmission delay results in an almost flat diversity-multiplexing tradeoff, and hence, renders operating at high multiplexing gain more advantageous; 2) MIMO ARQ channels quickly approach the ergodic limit when power control is employed. Finally, we complement our information-theoretic analysis with an incremental redundancy lattice space-time (IR-LAST) coding scheme which is shown, through a random coding argument, to achieve the optimal tradeoff(s). An integral component of the optimal IR-LAST coding scheme is a list decoder, based on the minimum mean-square error (MMSE) lattice decoding principle, for joint error detection and correction. Throughout the paper, our theoretical claims are validated by numerical results Control strategies for systems with information bottlenecks often follow an estimate-then-control paradigm. This paper presents a “non-coherent” system where this strategy cannot work and provides an alternative. The paper considers the estimation and control of a discrete-time linear system with continuous random observation gain, i.e. through a non-coherent channel. It is shown that such an unstable system is not mean-squared observable regardless of the density of the random observation gain: the mean-squared estimation error for any estimator must go to infinity. This is surprising in the context of threshold results for rate-limited estimation. In contrast to other results with rate-limited feedback, the paper shows that the system can be closed-loop mean-square stabilized in a certain parameter regime even though its open-loop counterpart is not mean-square observable. Finally, carry-free models (generalized deterministic models) provide an intuitive interpretation for the results. Spectrum management is used to improve performance in multiuser communication system, e.g., cognitive radio or femtocell networks, where multiuser interference can lead to data rate degradation. We study the nonconvex NP-hard problem of maximizing a weighted sum rate in a multiuser Gaussian interference channel by power control subject to affine power constraints. By exploiting the fact that this problem can be restated as an optimization problem with constraints that are spectral radii of specially crafted nonnegative matrices, we derive necessary and sufficient optimality conditions and propose a global optimization algorithm based on the outer approximation method. Central to our techniques is the use of nonnegative matrix theory, e.g., nonnegative matrix inequalities and the Perron-Frobenius theorem. We also study an inner approximation method and a relaxation method that give insights to special cases. Our techniques and algorithm can be extended to a multiple carrier system model, e.g., OFDM system or receivers with interference suppression capability.