State-space approach to nonlinear predictive generalized minimum variance control

A Nonlinear Predictive Generalized Minimum Variance (NPGMV) control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time-domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process but because of the assumed structure of the system the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well known GPC controller

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs

Effects in polarimetry of interference within wave plates

Multiple-beam interference within wave plates is investigated in terms of the detrimental effects it produces in the data of stellar spectropolarimetry. It is noted that spectral fringe structures occur in the phase delay, the polarizance and, for Pancharatnam designs, the reference axis of the wave plate. The natures of the problems are exposed by considering typical wave plates and experimental procedures used in linear and circular spectropolarimetry. It is demonstrated that the chief bane of accurate measurements is the presence of polarizance fringes, but which can be alleviated by the choice of experimental procedure. For spectral circular polarization studies, problems of cross-talk from any linear polarization present in the source are especially severe. In principle the effects of fringing can be removed in data reductions by calibration measurements of a set of linear polarization standard stars displaying different vibration azimuths and, for circular polarization measurements, knowledge of the linear polarization characteristics of the investigated star must also be known