The emerging area of control with limited data rates incorporates ideas from both control and information theory. The data rate constraint introduces quantization into the feedback loop and gives the interconnected system a two-fold nature, continuous and symbolic. In this paper, we review the results available in the literature on data-rate-limited control. For linear systems, we show how fundamental tradeoffs between the data rate and control goals, such as stability, mean entry times, and asymptotic state norms, emerge naturally. While many classical tools from both control and information theory can still be used in this context, it turns out that the deepest results necessitate a novel, integrated view of both disciplines

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.

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-limited 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 expression for LTFE in terms of the unstable eigenvalues of the fixed point Jacobian.

This paper presents an integrated probabilistic data association algorithm which provides recursive formulas for both data association and track quality (probability of track existence), allowing track initiation and track termination to be fully integrated into the association and smoothing algorithm. Integrated probabilistic data association is of similar computational complexity to probabilistic data association and as demonstrated by simulation, achieves comparable performance to the more computationally expensive interactive multiple model probabilistic data association algorithm which also integrates initiation and tracking.

A new recursive filter for multi-target tracking in clutter is presented. Multiple tracks may share the same measurement(s). Joint events are formed by creating all possible combinations of track-measurement assignments and the probabilities for these joint events are calculated. The expressions for the joint event probabilities incorporate the probabilities of target existence of individual tracks, an efficient approximation for the cluster volume and a priori probability of the number of clutter measurements in each cluster. From these probabilities the data association and target existence probabilities of individual tracks are obtained, which allows track state update and false track discrimination. A simulation study is presented to show the effectiveness of this approach.