Optimal Hankel Norm Model Reduction by Truncation of Trajectories

We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the past and future in the input-output pairs relating to left- and right singular vectors of the system. A self-contained proof of optimality is given, and formulas are derived in terms of Faddeev sequences. Some parallels with the literature are briefly indicated.Optimal Hankel norm approximation;Balancing;Linear systems;l2-systems;Faddeev sequences

Nonlinear three wave interaction in pair plasmas

It is shown that nonlinear three-wave interaction, described by vector-product type nonlinearities, in pair plasmas implies much more restrictive conditions for a double energy transfer, as compared to electron-ion plasmas

D-region differential-phase measurements and ionization variability studies

Measurements of electron densities in the D region are made by the partial-reflection differential-absorption and differential-phase techniques. The differential-phase data are obtained by a hard-wired phase-measuring system. Electron-sensity profiles obtained by the two techniques on six occasions are plotted and compared. Electron-density profiles obtained at the same time on 30 occasions during the years 1975 through 1977 are averaged to form a single profile for each technique. The effect of varying the assumed collision-frequency profile on these averaged profiles is studied. Time series of D-region electron-sensity data obtained by 3.4 minute intervals on six days during the summer of 1977 are examined for wave-like disturbances and tidal oscillations

Investigation of the winds and electron concentration variability in the D region of the ionosphere by the partial-reflection radar technique

The development and first observations of the partial-reflection drifts experiment at Urbana, Illinois (40 N) are described. The winds data from the drifts experiment are compared with electron concentration data obtained by the differential-absorption technique to study the possible meteorological causes of the winter anomaly in the mesosphere at midlatitudes. winds data obtained by the meteor-radar experiment at Urbana are also compared with electron concentration data measured at Urban. A significant correlation is shown is both cases between southward winds and increasing electron concentration measured at the same location during winter. The possibility of stratospheric/mesospheric coupling is investigated by comparing satellite-measured 0.4 mbar geopotential data with mesospheric electron concentration data. No significant coupling was observed. The winds measured at Saskatoon, Saskatchewan (52 N) are compared with the electron concentrations measured at Urban, yielding constant fixed relationship, but significant correlations for short segments of the winter. A significant coherence is observed at discrete frequencies during segments of the winter

Nonlinear polarisation and dissipative correspondence between low frequency fluid and gyrofluid equations

The correspondence between gyrofluid and low frequency fluid equations is examined. The lowest order conservative effects in ExB advection, parallel dynamics, and curvature match trivially. The principal concerns are polarisation fluxes, and dissipative parallel viscosity and parallel heat fluxes. The emergence of the polarisation heat flux in the fluid model and its contribution to the energy theorem is reviewed. It is shown that gyroviscosity and the polarisation fluxes are matched by the finite gyroradius corrections to advection in the long wavelength limit, provided that the differences between gyrocenter and particle representations is taken into account. The dissipative parallel viscosity is matched by the residual thermal anisotropy in the gyrofluid model in the collision dominated limit. The dissipative parallel heat flux is matched by the gyrofluid parallel heat flux variables in the collision dominated limit. Hence, the gyrofluid equations are a complete superset of the low frequency fluid equations.Comment: RevTeX 4, 28 pages, no figures, final revised version for Physics of Plasmas prior to proof stag

A behavioral approach to balanced representations of dynamical systems

AbstractThe behavioral approach to linear systems provides an alternative framework for studying the notion of balanced representations. A new definition for balanced representations is proposed that is one-to-one related to a set of system invariants that is obtained by assuming a specific Hilbert space structure on the system behavior. This notion of balancing is more general than the prevailing notion of balancing in that it is well defined for nonstable systems and is independent of a particular (input-output) representation of the system. It is shown that Lyapunov, LQ̧G, and H∞ balanced representations are obtained as a special case. An application for the problem of model approximation is discussed

A method of optimal system identification with applications in control

In this paper an optimal deterministic identification problem is solved in which a new measure for the misfit between data and system is minimized. It is shown that the misfit can be expressed as the Hankel norm of a specific operator. Optimal autonomous models are obtained by factorizing an optimal Hankel norm approximant of the Laplace transformed data matrix. An upper bound on the misfit between model and data is derived for a class of non-autonomous models of prescribed complexity. The identified autonomous systems are viewed as closed-loop behaviors of a feedback interconnection of two systems. Stability of these feedback interconnections is discussed

Amending the National Environmental Policy Act: Federal Environmental Protection in the Twenty-First Century

The National Environmental Policy Act (NEPA) represents the cornerstone of American environmental law and marks the beginning of the environmental law statutory movement in the United States. This Article traces the evolution of NEPA and the environmental movement and describes the framers\u27 intent in passing NEPA. Next, the Article examines judicial and executive interpretations of NEPA. The Article concludes by assessing NEPA\u27s present state and suggesting possible reforms to ensure a strong future commitment to NEPA