Journals:
X. Ma, S.M. Djouadi, C.D. Charalambous “Optimal Filtering Over Uncertain Wireless Communication Channels,” IEEE Signal Processing Letters, Vol.18, No.6, pp.359-362, June 2011
Abstract
In this letter, filtering over wireless communication channels subject to packet losses is considered. The packet losses are assumed to follow a Bernoulli distribution. The latter is interpreted as a special case of a Markov process for which hybrid filtering theory is shown to provide an exact solution. Unlike existing works where only the linear optimal state estimate is derived as a linear function of measurements, this paper shows that the optimal state estimate is in fact a nonlinear function of measurements. In addition, the optimal estimator is derived explicitly. Illustrative examples compare the performance of the linear optimal estimator and the optimal estimator, and show that the latter offer superior performance, in particular for unstable systems.
A. Farhadi and C.D. Charalambous, “Stability and Reliable Data Reconstruction of Uncertain Dynamical Systems over Finite Capacity Channels,” Automatica, Vol.46, No.5, pages 889-896, May 2010
Abstract
In this paper we present an encoder, decoder and a stabilizing controller for reliable data reconstruction and robust stability of uncertain dynamic systems controlled over Additive White Gaussian Noise (AWGN) channels. The uncertainty in the dynamic system is described by a relative entropy constraint. Such an uncertainty description is a natural stochastic generalization of the sum quadratic uncertainty description. This paper complements the results of Farhadi and Charalambous (2008) by showing that the necessary condition presented there can be tight. This is shown by designing an encoder, decoder and a stabilizing controller. © 2010 Elsevier Ltd. All rights reserved.
A. Farhadi and C.D. Charalambous, “Robust Coding for a Class of Sources: Applications in Control and Reliable Communication Over Limited Capacity Channels,” Systems and Control Letters, 57, pp.1005-1012, 2008
Abstract
This paper is concerned with the control of a class of dynamical systems over finite capacity communication channels. Necessary conditions for reliable data reconstruction and stability of a class of dynamical systems are derived. The methodology is information theoretic. It introduces the notion of entropy for a class of sources, which is defined as a maximization of the Shannon entropy over a class of sources. It also introduces the Shannon information transmission theorem for a class of sources, which states that channel capacity should be greater or equal to the mini-max rate distortion (maximization is over the class of sources) for reliable communication. When the class of sources is described by a relative entropy constraint between a class of source densities, and a given nominal source density, the explicit solution to the maximum entropy, is given, and its connection to Rényi entropy is illustrated. Furthermore, this solution is applied to a class of controlled dynamical systems to address necessary conditions for reliable data reconstruction and stability of such systems.
C.D. Charalambous and A. Farhadi, “LQG Optimality and Separation Principle for General Discrete-Time Partially Observed Stochastic Systems over Finite Capacity Communication Channels,” Automatica, 44, pp.3181-3188, 2008
Abstract
This paper is concerned with control of stochastic systems subject to finite communication channel capacity. Necessary conditions for reconstruction and stability of system outputs are derived using the Information Transmission theorem and the Shannon lower bound. These conditions are expressed in terms of the Shannon entropy rate and the distortion measure employed to describe reconstruction and stability. The methodology is general, and hence it is applicable to a variety of systems. The results are applied to linear partially observed stochastic Gaussian controlled systems, when the channel is an Additive White Gaussian Noise (AWGN) channel. For such systems and channels, sufficient conditions are also derived by first showing that the Shannon lower bound is exactly equal to the rate distortion function, and then designing the encoder, decoder and controller which achieve the capacity of the channel. The conditions imposed are the standard detectability and stabilizability of Linear Quadratic Gaussian (LQG) theory, while a separation principle is shown between the design of the control and communication systems, without assuming knowledge of the control sequence at the encoder/decoder. Crown Copyright © 2008.
C.D. Charalambous, A. Farhadi and D. Stojan, “Control of Continuous Time Linear Gaussian Systems over Additive Gaussian Wireless Fading Channels: A Separation Principle,” IEEE Transactions on Automatic Control, Vol. 53, No.4, pages 1013-1019, 2008.
Abstract
This note is concerned with the control of continuous-time linear Gaussian systems over additive white noise wireless fading channels subject to capacity constraints. Necessary and sufficient conditions are derived, for bounded asymptotic and asymptotic observability and stabilizability in the mean square sense, for controlling such systems. For the case of a noiseless time-invariant system controlled over a continuous-time additive white Gaussian noise channel, the sufficient condition for stabilizability and observability states that the capacity of the channel C must satisfy C > Sigma {i;Re(lambdai(A))ges0} Re(lambda i (A)), where A is the system matrix and lambda i (A) denotes the eigenvalues of A. The necessary condition states that the channel capacity must satisfy C ges Sigma {i;Re(lambdai(A))ges0} Re(lambda i (A)). Further, it is shown that a separation principle holds between the design of the communication and the control subsystems, implying that the controller that would be optimal in the absence of the communication channel is also optimal for the problem of controlling the system over the communication channel.
Conferences:
C.D. Charalambous, C. Kourtellaris, C. Hadjicostis, “Optimal Encoder and Controller Strategies in Stochastic Control Subject to Rate Constraints for Channels with Memory and Feedback: Dynamic Programming,” in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, U.S.A., December 12-15, pp. 4522-4527, 2011
Abstract
This paper is concerned with the joint design of encoder/control strategies which minimize a control payoff subject to a rate constraint on the feedback information provided by the system. The control system is described by a conditional distribution, while the rate is described by the directed information of a noisy communication channel. By generalizing the Posterior Matching Scheme (PMS), a scheme that achieves operational capacity, to channels with memory and feedback, the joint optimality of encoder/control strategies is analyzed. A principle of optimality is derived and a dynamic programming equation is obtained, which together describe how the optimal encoder/control strategies should be selected. It is shown that joint optimality separates into an optimal encoder strategy based on the PMS, and a control strategy obtained via the dynamic programming equation.
C.D. Charalambous, C. Kourtellaris, C. Hadjicostis, “Optimal Encoders Maximizing Directed Information of Channels with Memory and Feedback: Control and Dynamic Programming,” in Proceeding of the 18th World Congress of the International Federation of Automatic Control, Milano, Italy, August 28-September 2, 2011 (Invited Session)
C.D. Charalambous, “Uncertain Stochastic Systems on Abstract Spaces: Applications to Control and Communication Systems,” in 4th International Symposium on Communication, Control and Signal Processing, Limassol, Cyprus, March 3-March 5, 2010
C.D. Charalambous, I. Kourtellaris, F. Stavrou, “Stochastic Control Over Finite Capacity Channels: Causality, Feedback, and Uncertainty,” in Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp.5889-5894, Shanghai, China, December 16-18, 2009
Abstract
Optimal communication/control analysis and design of dynamical controlled systems, when there are finite capacity communication constraints often involve information and control theoretic analysis. This paper, employees information theoretic concepts to develop a mathematical framework for analysis and design of optimal communication/control system subject to uncertainty, causality and feedback. The theory is developed by generalizing the classical information theoretic theorems of Shannon to their robust analogs. Necessary conditions for stability and reconstruction of uncertain control signals over uncertain channels are presented via the causal rate distortion function for a family of sources and channel capacity for a family of channels. Further, in view of the complexity of the causal rate distortion function, a tight lower bound is introduced which applies to families of sources. Finally, using a generalized version of the information transmission theorem and the lower bound on the rate distortion function, the connection between stabilizabilty and reconstruction is related to capacity for a class of channels.
C.D. Charalambous and C. Kourtellaris, “Information Theory for Control Systems: Causality and Feedback,” in 2009 European Control Conference, pp.35-60, December 9-11, 2009, Budapest, Hungary
A. Farhadi and C.D. Charalambous, “Robust Stabilizing Scheme for Uncertain Systems Controlled over Limited Capacity Additive White Gaussian Noise Channels,” in Proceedings of the 2008 American Control Conference, Seattle, Washington, U.S.A., June 11-13, 2008
Abstract
In this paper we propose an encoding scheme and a stability scheme for reliable data reconstruction and robust stability of uncertain dynamical systems controlled over Additive White Gaussian Noise (AWGN) channels subject to limited capacity constraints. The uncertainty in the dynamical system is described by a relative entropy constraint. Specifically, the design of an encoder, decoder and controller that stabilize an uncertain system subject to the sum quadratic uncertainty description, is considered.
A. Farhadi and C.D. Charalambous, “Robust Control of a Class of Feedback Systems Subject to Limited Capacity Constraints,” in 2007 Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, U.S.A., December 12-14, 2007
Abstract
In this paper we are concerned with uniform mean square reliable data reconstruction and robust stability for a class of dynamical systems over additive white Gaussian noise (AWGN) channels, subject to the limited capacity constraints. Specifically, the design of an encoder, decoder and controller subject to the mean square reliable data reconstruction and stability, is considered for a class of dynamical systems. The class of dynamical systems which are described the uncertainty is modeled via a relative entropy constraint.
Stojan Denic and C.D. Charalambous, “Control of Jump Linear Systems over Jump Communication Channels: Source-Channel Matching Approach,” in 2007 IEEE International Symposium on Information Theory, pages 2491-2495, Nice, France, June 24-27, 2007
Abstract
The control of partially observed jump linear systems over jump communication channels is investigated when the Plant State Information (PSI) and the Channel State Information (CSI) are present at the transmitter and the receiver side of the communication channel. The PSI refers to the state of a Markov chain driving the plant dynamics, while the CSI is the state of a Markov chain driving the communication channel. Necessary conditions for observability and stabilizability in probability and r-th mean are derived by using information transmission theorem and Shannon's lower bound on the rate distortion. Based on the source-channel matching principle, a transmission technique is designed that achieves observability and stabilizability of the controlled jump system in mean-square sense.
C.D. Charalambous, A. Farhadi, “Control of Feedback Systems Subject to Finite Rate Constraints via the Shannon Lower Bound,”The 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks , pp.1886-1893, 2007
Abstract
This paper is concerned with control of stochastic systems subject to limited feedback channel capacity. Specifically, the design of an encoder, decoder, and controller subject to the mean square observability and stabilizability is considered. It is shown that by transmitting information which is equal to the Shannon lower bound, mean square observability and stabilizability over Additive White Gaussian Noise (AWGN) channel is achieved. Furthermore, a modified definition for channel capacity and rate distortion is presented which is suitable for control applications and real time communication.
S. Denic, C.D. Charalambous, “Control of Discrete-Time Partially-Observed Jump Linear Systems Over Causal Communication Systems,” in Proceedings of the 45th IEEE Conference on Decision and Control, pages 496-501, San Diego, California, December, 2006
Abstract
We consider the problem of control of discrete-time partially-observed jump linear system over a noisy causal communication channel. Necessary conditions for observability and stabilizability in probability and r-th mean of a jump linear system driven by a Markov chain are derived. The methodology is information theoretic and it is based on an alternative definition of mutual information between two random processes which is restricted to a causal channel. Specifically, the self-mutual information is restricted to Radon-Nykodym derivatives corresponding to causal channels. This gives rise to information capacity and rate distortion formulaes which involve causal operations, leading to a new set of data processing inequalities.
A. Farhadi and C.D. Charalambous, “Control of Tele-Operation Systems Subject to Capacity Limited Channels and Uncertainty,” 2006 IEEE Canadian Conference on Electrical Engineering (CCECE), pp. 1019-1024, Ottawa, Canada, May 7-10, 2006
Abstract
This paper is concerned with asymptotic observability and stabilizability of dynamical systems over communication channels subject to limited transmission capacity constraint and uncertainty. In particular, the following control/communication systems are considered. 1) The control/communication system described by a controlled diffusion process over an additive white Gaussian noise (AWGN) flat fading channel subject to limited transmission capacity constraint, in which, the sensors are geographically separated from the plant while the controller is attached to the plant, and 2) The control/communication system described by an uncertain plant over uncertain communication channels subject to limited transmission capacity constraint, in which, there is communication constraint in both forward and feedback paths.
C.D. Charalambous and A. Farhadi, “A Mathematical Framework for Robust Control over Uncertain Communication Channels,” in Proceedings of the 2005 IEEE Conference on Decision and Control and European Conference on Control (CDC-ECC’s), pp.2530-2535, Seville, Spain, December 12-15, 2005. (invited session paper)
Abstract
In this paper, a mathematical framework for studying robust control over uncertain communication channels is introduced. The theory is developed by 1) Generalizing the classical information theoretic measures to the robust analogous, which are subject to uncertainty in the source and the communication channel, 2) Deriving a lower bound for the robust rate distortion, and 3) Finding a necessary condition on the communication blocks subject to uncertainty for reliable communication up to distortion level D v . By invoking this mathematical framework, necessary conditions for uniform asymptotic observability and stabilizability are derived for the following uncertain plants controlled over uncertain communication channels. 1) A probabilistic uncertain plant defined via a relative entropy constraint and 2) A frequency domain uncertain plant defined via an H ∞ constraint.
C.D. Charalambous and S. Denic and A. Farhadi, “Control of Continuous-Time Systems over Wireless Communication Channels,” in Proceedings of the 2005 IEEE Conference on Decision and Control and European Conference on Control (CDC-ECC’s), pp.3225-3230, Seville, Spain, December 12-15, 2005.(invited session paper)
Abstract
This note is concerned with the control of continuous-time linear Gaussian systems over additive white noise wireless fading channels subject to capacity constraints. Necessary and sufficient conditions are derived, for bounded asymptotic and asymptotic observability and stabilizability in the mean square sense, for controlling such systems. For the case of a noiseless time-invariant system controlled over a continuous-time additive white Gaussian noise channel, the sufficient condition for stabilizability and observability states that the capacity of the channel C must satisfy C > Sigma {i;Re(lambdai(A))ges0} Re(lambda i (A)), where A is the system matrix and lambda i (A) denotes the eigenvalues of A. The necessary condition states that the channel capacity must satisfy C ges Sigma {i;Re(lambdai(A))ges0} Re(lambda i (A)). Further, it is shown that a separation principle holds between the design of the communication and the control subsystems, implying that the controller that would be optimal in the absence of the communication channel is also optimal for the problem of controlling the system over the communication channel.
C.D. Charalambous and A. Farhadi, “Robust Entropy Rate for Uncertain Sources: Application to Communication and Control Systems,” in Proceedings of the 2005 Canadian Workshop on Information Theory, pp. Montreal, Quebec, Canada, July 4-9, 2005
Abstract
In this paper the notion of robust entropy and subsequently, robust entropy rate for a family of discrete time uncertain sources is introduced. When the uncertainty is described by a relative entropy constraint between the set of uncertain source densities and a given nominal source density, the solution to this robust notion of information is presented and its connection with other notions of entropy definitions, such as, Renyi entropy and Tsallis entropy is presented. Then, the robust entropy rate is calculated for 1) Uncertain sources corresponding to a partially observed Gauss Markov process, 2) Sources with uncertain frequency response, and 3) Uncertain sources corresponding to a partially observed controlled Gauss Markov Process. Finally, an application of the robust entropy rate in networked control systems is presented by defining necessary conditions for uniform asymptotic stabilizability and observability.
