Methodological Remarks on CPG-Based Control of Flapping Flight

This paper is a companion to Chung and explores the applications of neurobiologically inspired control systems in the form of Central Pattern Generators (CPG) to control flapping flight dynamics. We introduce two-layer CPGs to mimic current hypotheses of mammalian studies. It is shown that symmetry breaking to initiate and recover from a turning maneuver is an effective control strategy. Attempts at dissociating slow dynamics are shown and preliminary comparisons of wing motions between biological fliers and artificial CPG networks are made

Moments of Random Variables: A Systems-Theoretic Interpretation

Moments of continuous random variables admitting a probability density function are studied. We show that, under certain assumptions, the moments of a random variable can be characterised in terms of a Sylvester equation and of the steady-state output response of a specific interconnected system. This allows to interpret well-known notions and results of probability theory and statistics in the language of systems theory, including the sum of independent random variables, the notion of mixture distribution and results from renewal theory. The theory developed is based on tools from the center manifold theory, the theory of the steady-state response of nonlinear systems, and the theory of output regulation. Our formalism is illustrated by means of several examples and can be easily adapted to the case of discrete and of multivariate random variables

Steady-state behaviors in nonlinear systems with an application to robust disturbance rejection

Despite the widespread intuitive appeal of the concept of steady-state response and its use in shaping the asymptotic behavior of control systems, this concept has only been rigorously defined for finite-dimensional, linear time invariant systems. In this paper, we investigate this concept for nonlinear systems, following some classical developments in nonlinear dynamics. As an application, we show how the concept in question plays a role of paramount importance in the design of control laws for asymptotic tracking and disturbance attenuation. (C) 2008 Elsevier Ltd. All rights reserved