Robin J. Evans

Feedback Control Under Data Rate Constraints: An Overview

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

Integrated probabilistic data association

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. >

Stabilization with data-rate-limited feedback : tightest attainable bounds

Abstract This paper investigates the stabilizability of a linear, discrete-time plant with a real-valued output when the controller, which may be nonlinear, receives observation data at a known rate. It is first shown that, under a finite horizon cost equal to the m th output moment, the problem reduces to quantizing the initial output. Asymptotic quantization theory is then applied to directly obtain the limiting coding and control scheme as the horizon approaches infinity. This is proven to minimize a particular infinite horizon cost, the value of which is derived. A necessary and sufficient condition then follows for there to exist a coding and control scheme with the specified data rate that takes the m th output moment to zero asymptotically with time. If the open-loop plant is finite-dimensional and time-invariant, this condition simplifies to an inequality involving the data rate and the unstable plant pole with greatest magnitude. Analagous results automatically hold for the related problem of state estimation with a finite data rate.

Topological feedback entropy and Nonlinear stabilization

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 Shannons 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.

Control of chaos: Methods and applications in engineering

Abstract A survey of the emerging field termed “control of chaos” is given. Several major branches of research are discussed in detail: feedforward or “nonfeedback control” (based on periodic excitation of the system); “OGY method” (based on linearization of the Poincare map), “Pyragas method” (based on a time-delay feedback), traditional control engineering methods including linear, nonlinear and adaptive control, neural networks and fuzzy control. Some unsolved problems concerning the justification of chaos control methods are presented. Other directions of active research such as chaotic mixing, chaotization, etc. are outlined. Applications in various fields of engineering are discussed.

Stability results for switched controller systems

There are many practical control problems where the control action is determined by switching among a given set of control laws. This paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems. Algorithms which can be used to construct appropriately stabilizing control laws are also presented.

Joint integrated probabilistic data association: JIPDA

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.

Optimal waveform selection for tracking systems

Investigates adaptive waveform selection schemes where selection is based on overall target tracking system performance. Optimal receiver assumptions allow the inclusion of transmitted waveform specification parameters in the tracking subsystem defining equations. The authors give explicit expressions for two one-step ahead optimization problems for a single target in white Gaussian noise when the tracker is a conventional Kalman filter. These problems may be solved to yield the most improvement possible in tracking performance for each new transmitted pulse. In cases where target motion is restricted to one dimension, closed-form solutions to the local (one step ahead) waveform optimization problem have been obtained. The optimal waveform selection algorithms in the paper may be included with conventional Kalman filtering equations to form an enhanced Kalman tracker. Simulation examples are presented to illustrate the potential of the waveform selection schemes for the optimal utilization of the capabilities of modern digital waveform generators, including multiple waveform classes. The extension of the basic waveform optimization scheme to more complex tracking scenarios is also discussed. >

Robust pole assignment

Abstract This paper presents new theorems on the theory of interval matrix inequalities and the theory of polynomials with interval roots, and applies them to the problem of robust pole-placement. We formulate optimization problems and derive convergent iterative algorithms which allow the designer to find controllers that place closed-loop poles within desired intervals for plants with unknown-but-bounded parameter uncertainties. The algorithms are computationally reasonable and provide a useful addition to currently existing control CAD tools.

Waveform selective probabilistic data association

An adaptive, waveform selective probabilistic data association (WSPDA) algorithm for tracking a single target in clutter is presented. The assumption of an optimal receiver allows the inclusion of transmitted waveform specification parameters in the tracking subsystem equations, leading to a waveform selection scheme where the next transmitted waveform parameters are selected so as to minimize the average total mean-square tracking error at the next time step. Semiclosed form solutions are given to the local (one-step-ahead) adaptive waveform selection problem for the case of one-dimensional target motion. A simple simulation example is given to compare the performance of a tracking system using a WSFDA based tracking filter with that of a conventional system with a fixed waveform shape and probabilistic data association (PDA) tracking filter.