Finite Capacity Communication Channels Research Articles

Two Lyapunov methods in nonlinear state estimation via finite capacity communication channels

The paper deals with observation of nonlinear and deterministic, though maybe chaotic, continuous-time systems via finite capacity communication channels.

Observation of nonlinear systems via finite capacity channels: Constructive data rate limits

The paper deals with observation of nonlinear and deterministic, though maybe chaotic, discrete-time systems via finite capacity communication channels. We introduce several minimum data-rate limits associated with various types of observability, and offer new tractable analytical techniques for their both upper and lower estimation. Whereas the lower estimate is obtained by following the lines of the Lyapunov’s linearization method, the proposed upper estimation technique is along the lines of the second Lyapunov approach. As an illustrative example, the potential of the presented results is demonstrated for the system which describes a ball vertically bouncing on a sinusoidally vibrating table. For this system, we provide an analytical computation of a closed-form expression for the threshold that separates the channel data rates for which reliable observation is and is not possible, respectively. Another illustration is concerned with the celebrated Hénon system. The offered sufficient data rate bound is accompanied with a constructive observer that works whenever the channel capacity fits this bound.

Data rate limitations for observability of nonlinear systems

The paper deals with observation of nonlinear and deterministic, though maybe chaotic, discrete-time systems via finite capacity communication channels. We consider various types of observability, and offer new tractable analytical techniques for both upper and lower estimation of the threshold that separates data rates for which reliable state observation is and is not possible, respectively. The main results are illustrated via their application to two celebrated samples of chaotic systems associated with the logistic and Lozi maps, respectively. In these cases, the thresholds attributed to some of the considered notions of observability are found in a closed form; they are shown to continuously depend on the parameters of the Lozi system.

LQG optimality and separation principle for general discrete time partially observed stochastic systems over finite capacity communication channels

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.

Robust coding for a class of sources: Applications in control and reliable communication over limited capacity channels

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.

Remote tracking via encoded information for nonlinear systems

The problem addressed in this paper is to control a plant so as to have its output tracking (a family of) reference commands generated at a remote location and transmitted through a communication channel of finite capacity. The uncertainty due to the presence of the communication channel is counteracted by a suitable choice of the parameters of the regulator.

DELAY DEPENDENT STOCHASTIC STABILITY AND APPLICATION IN CONTROL WITH LIMITED COMMUNICATION

A theorem by de Souza on stochastic stability of systems with delays has been strengthened. This result provides a condition for delay-dependent stability. As in many practical applications a realistic bound on the delay may be known such a result should be useful where simple delay-independent stability conditions fail. In particular, this has ramifications in the robustness of stability of systems controlled over finite capacity communication channels.

Quantization of the rolling-body problem with applications to motion planning

The problem of manipulation by low-complexity robot hands is a key issue since many years. The performance of simplified hardware manipulators relies on the exploitation of nonholonomic effects that occur in rolling. Beside this issue, more recently, the attention of the scientific community has been devoted to the problems of finite capacity communication channels and of constraints on the complexity of computation. Quantization of controls proved to be efficient for dealing with such kinds of limitations. With this in mind, we consider the rolling of a pair of smooth convex objects, one on top of the other, under quantized control. The analysis of the reachable set is performed by exploiting the geometric nature of the system which helps in reducing to the case of a group acting on a manifold. The cases of a plane, a sphere and a body of revolution rolling on an arbitrary surface are treated in detail.

Multirate Stabilization of Linear Multiple Sensor Systems via Limited Capacity Communication Channels

The paper addresses a feedback stabilization problem involving bit-rate communication capacity constraints. A discrete-time partially observed linear system is studied. Unlike classic theory, the signals from multiple sensors are transmitted to the controller over separate finite capacity communication channels. The sensors do not have constant access to the channels, and the channels are not perfect: the messages incur time-varying transmission delays and may be corrupted or lost. However, we suppose that the time-average number of bits per sample period that can be successfully transmitted over the channel during a time interval converges to a certain limit as the length of the interval becomes large. Necessary and sufficient conditions for stabilizability are established. They give the tightest lower bounds on the channel capacities for which stabilization is possible. An algorithm for stabilization is also presented.

Quantum measurement as a communication with nature

It is assumed that experiments yield results that are not isomorphic with reality, but represent a distorted image of reality. Reality is related to observation via a communication channel of finite capacity. Quantum uncertainties are due to the bound on the amount of information available. Use is made of recent results from information and communication theories.