Dead-beat control of simple Hammerstein models

Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonminimum-time state dead-beat controllers are given for certain classes of simple Hammerstein systems. A general minimum-time state dead-beat controller is presented for a class of simple Hammerstein systems. A design for a family of minimum-time control laws is provided. This enables, to a certain extent, shaping of transient response via choosing an appropriate control law. Finally, the authors design an output dead-beat controller for a class of Hammerstein systems that are not necessarily state dead-beat controllable     

Online learning via congregational gradient descent

We propose and analyse a populational version of stepwise gradient descent suitable for a wide range of learning problems. The algorithm is motivated by genetic algorithms which update a population of solutions rather than just a single representative as is typical for gradient descent. This modification of traditional gradient descent (as used, for example, in the backpropogation algorithm) avoids getting trapped in local minima. We use an averaging analysis of the algorithm to relate its behaviour to an associated ordinary differential equation. We derive a result concerning how long one has to wait in order that, with a given high probability, the algorithm is within a certain neighbourhood of the global minimum. We also analyse the effect of different population sizes. An example is presented which corroborates our theory very well.This work was supported by the Australian Research Council.     

Necessary conditions for stability and attractivity of continuous systems

Considered in this paper are control systems of the form ? =f(x, u). For such systems a number of related necessary conditions for various forms of stability and attractivity are presented. The paper starts by showing that Brockett’s necessary condition for stabilizability via smooth feedback still persists if/ is continuous and the class of allowable u increased to include continuous feedbacks. Using similar ideas to those used to prove the continuous Brockett result, again only assuming continuity of f and u, necessary conditions are then derived for global attractivity and for ultimate boundedness.     

Non-local stabilization of a spherical inverted pendulum

We design a non-linear stabilizing control law for a four degree of freedom spherical inverted pendulum. The pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint; the joint is free to move in the plane under the influence of a planar force. The upright position is an unstable equilibrium of the uncontrolled system because of gravity. The objective is to design a controller so that it stabilizes the upright position starting from any position in the upper hemisphere with arbitrary velocity. We achieve this by first transforming the original system to an appropriate upper triangular form and then designing a controller which incorporates a high gain design with the method of non-linear forwarding. The control law is evaluated through computer simulations.     

How exciting can a signal really be?

The rate of parameter convergence in a number of adaptive estimation schemes is related to the smallest eigenvalue of the average information matrix determined by the regression vector. Using a very simple examples, we illustrate that the input signals that maximize this minimum eigenvalue may be quite different from the input signals that optimize more classical input design criteria, e.g. D-optimal criterion.     

Nonlinear averaging theorems, and the determination of parameter convergence rates in adaptive control

The paper presents nonlinear averaging theorems for two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are applied to the Narendra-Valavani adaptive control algorithm, and estimates of the parameter convergence rates are obtained which do not rely on a linearization of the system around the equilibrium, and therefore are valid in a larger region in the parameter space.     

Influence of central command and ergoreceptors on the splanchnic circulation during isometric exercise

The splanchnic circulation can make a major contribution to blood flow changes. However, the role of the splanchnic circulation in the reflex adjustments to the blood pressure increased during isometric exercise is not well documented. The central command and the muscle chemoreflex are the two major mechanisms involved in the blood pressure response to isometric exercise. This study aimed to examine the behaviour of the superior mesenteric artery during isometric handgrip (IHG) at 30% maximal voluntary contraction (MVC). The pulsatility index (PI) of the blood velocity waveform of the superior mesenteric artery was taken as the study parameter. A total of ten healthy subjects [mean age, 21.1 (SEM 0.3) years] performed an IHG at 30% MVC for 90 s. At 5 s prior to the end of the exercise, muscle circulation was arrested for 90 s to study the effect of the muscle chemoreflex (post exercise arterial occlusion, PEAO). The IHG at 30% MVC caused a decrease in superior mesenteric artery PI, from 4.84 (SEM 1.57) at control level to 3.90 (SEM 1.07) (P = 0.015). The PI further decreased to 3.17 (SEM 0.70) (P = 0.01) during PEAO. Our results indicated that ergoreceptors may be involved in the superior mesenteric artery vasodilatation during isometric exercise.     

Comparability problems in the analysis of multiway data

Almost all methods for the analysis of multiway data assume that the comparison of any two entries in the data array under study reflects or represents meaningful content-specific information. This is especially the case if one wants the data analysis to yield insight into the real mechanisms underlying the data. Violation of this assumption may imply data-analytic results that are of doubtful quality at best and worthless in the worst-case scenario. In the present paper, we first clarify why comparability is a key assumption in most methods for multiway data analysis. Next, we list a number of reasons why this assumption is very often violated in practice. We then review a few possible approaches that have been advanced to deal with problems of comparability, and discuss their advantages and shortcomings. We conclude by clarifying that any satisfactory solution to comparability problems requires a very careful reflection about the data collection and the ultimate goal of the data analysis.