A survey of models, analysis tools and compensation methods for the control of machines with friction

Natural evolution is a population-based optimization process. Simulating this process on a computer results in stochastic optimization techniques that can often outperform classical methods of optimization when applied to difficult real-world problems. There are currently three main avenues of research in simulated evolution: genetic algorithms, evolution strategies, and evolutionary programming. Each method emphasizes a different facet of natural evolution. Genetic algorithms stress chromosomal operators. Evolution strategies emphasize behavioral changes at the level of the individual. Evolutionary programming stresses behavioral change at the level of the species. The development of each of these procedures over the past 35 years is described. Some recent efforts in these areas are reviewed. >

An introduction to simulated evolutionary optimization

In this paper, we present new conditions ensuring existence, uniqueness, and Global Asymptotic Stability (GAS) of the equilibrium point for a large class of neural networks. The results are applicable to both symmetric and nonsymmetric interconnection matrices and allow for the consideration of all continuous nondecreasing neuron activation functions. Such functions may be unbounded (but not necessarily surjective), may have infinite intervals with zero slope as in a piece-wise-linear model, or both. The conditions on GAS rely on the concept of Lyapunov Diagonally Stable (or Lyapunov Diagonally Semi-Stable) matrices and are proved by employing a class of Lyapunov functions of the generalized Lur'e-Postnikov type. Several classes of interconnection matrices of applicative interest are shown to satisfy our conditions for GAS. In particular, the results are applied to analyze GAS for the class of neural circuits introduced for solving linear and quadratic programming problems. In this application, the principal result here obtained is that these networks are GAS also when the constraint amplifiers are dynamical, as it happens in any practical implementation. >

New conditions for global stability of neural networks with application to linear and quadratic programming problems

An overview is presented of several methods, filter structures, and recursive algorithms used in adaptive infinite-impulse response (IIR) filtering. Both the equation-error and output-error formulations are described, although the focus is on the adaptive algorithms and properties of the output-error configuration. These parameter-update algorithms have the same generic form, and they are based on a prediction-error performance criterion. A direct-form implementation of the adaptive filters is emphasized, but alternative realizations such as the parallel and lattice forms are briefly discussed. Several important issues associated with adaptive IIR filtering, including stability monitoring, the SPR condition, and convergence, are addressed. >

Adaptive IIR filtering

An integrated approach to the design of practical adaptive control algorithms is presented. Many existing ideas are brought together, and the effect of various design parameters available to a user is explored. The theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators. It is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics. >

Design issues in adaptive control

Stability of adaptive systems: passivity and averaging analysis

On a stability criterion for continuous slow adaptation

The instability of adaptive schemes at very low or even infinitesimal values of parameter adjustment gain has the form of a slow drift of adjustable parameters. With an averaging analysis we derive not only a sufficient condition for stability of this drift, but also a sufficient condition for it to be unstable. The result is a sharp boundary between stability and instability, which has a simple interpretation of signal energy.

A stability-instability boundary for disturbance-free slow adaptation and unmodeled dynamics

Examination of the SPR condition in output error parameter estimation

Stability bounds for fast and slow adaptation are derived for a simple adaptive system with one unmodelled (‘parasitic’) pole which is approximated by a right half-plane zero. In fast adaptation the product of the adaptive gain and power of the reference input must be smaller than the parasitic pole. In slow adaptation most of the input signal energy must be in the frequency range lower than the square root of the parasitic pole. It is shown that a plant bypass ensures a global stability property by making the linear time-invariant part of the adaptive loop strictly positive real (SPR). The price paid is an increase of the tracking error at very low frequencies and with slow adaptation when the equilibrium of the system without bypass is exponentially stable.

B. Riedle

Papers

Stability of adaptive systems: passivity and averaging analysis

On a stability criterion for continuous slow adaptation

A stability-instability boundary for disturbance-free slow adaptation and unmodeled dynamics

Examination of the SPR condition in output error parameter estimation

Stability analysis of an adaptive system with unmodelled dynamics