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NASA NTRS1991

A game theoretic approach to a finite-time disturbance attenuation problem

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.

Rhee, Ihnseok↗

NASA NTRS1992

Nonlinear techniques for forecasting solar activity directly from its time series

Numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series are presented. This approach makes it possible to extract dynamical invariants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), given a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.

Ashrafi, S.↗

NASA NTRS1991

Astrophysical aspects of Weyl gravity

This paper discusses the astrophysical implications and applications of Weyl gravity, which is the theory resulting from the unique action allowed under the principle of local scale invariance in Einstein gravity. These applications include galactic dynamics, the mass-radius relation, the cosmological constant, and the 'Modified Newtonian Dynamics' proposed by Milgrom (1983). The relation of Weyl gravity to other scale-invariant theories is addressed.

Kazanas, Demosthenes↗

NASA NTRS1991

Some characteristics of small-scale turbulence in a turbulent duct flow

The fine-scale structure of turbulence in a fully developed turbulent duct flow is examined by considering the 3D velocity derivative field obtained from direct numerical simulations at two relatively small Reynolds numbers. The magnitudes of all mean-square derivatives (normalized by wall variables) increase with the Reynolds number, the increase being largest at the wall. These magnitudes are not consistent with the assumption of local isotropy except perhaps near the duct center-line. When the assumption of local isotropy is relaxed to one of local axisymmetry, or invariance with respect to rotation about a coordinate axis (here chosen in the streamwise direction), satisfactory agreement is indicated by the data outside the wall region. Support for axisymmetry is demonstrated by anisotropy invariant maps of the dissipation and vorticity tensors.

Antonia, R. A.↗

NASA NTRS1990

Connectivity strategies for higher-order neural networks applied to pattern recognition

Different strategies for non-fully connected HONNs (higher-order neural networks) are discussed, showing that by using such strategies an input field of 128 x 128 pixels can be attained while still achieving in-plane rotation and translation-invariant recognition. These techniques allow HONNs to be used with the larger input scenes required for practical pattern-recognition applications. The number of interconnections that must be stored has been reduced by a factor of approximately 200,000 in a T/C case and about 2000 in a Space Shuttle/F-18 case by using regional connectivity. Third-order networks have been simulated using several connection strategies. The method found to work best is regional connectivity. The main advantages of this strategy are the following: (1) it considers features of various scales within the image and thus gets a better sample of what the image looks like; (2) it is invariant to shape-preserving geometric transformations, such as translation and rotation; (3) the connections are predetermined so that no extra computations are necessary during run time; and (4) it does not require any extra storage for recording which connections were formed.

Spirkovska, Lilly↗

NASA NTRS1992

Model reduction using new optimal Routh approximant technique

An optimal Routh approximant of a single-input single-output dynamic system is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is determined by minimizing a time-response integral-squared-error (ISE) criterion. In this paper, a new elegant approach is presented for obtaining the optimal Routh approximants for linear time-invariant continuous-time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear Routh approximants of linear time-invariant discrete-time systems. The proposed technique is simple in formulation and is amenable to practical implementation.

Hwang, Chyi↗

NASA NTRS1991

On lattice chiral gauge theories

The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations.

Maiani, L.↗

NASA NTRS1991

Automated target recognition and tracking using an optical pattern recognition neural network

The on-going development of an automatic target recognition and tracking system at the Jet Propulsion Laboratory is presented. This system is an optical pattern recognition neural network (OPRNN) that is an integration of an innovative optical parallel processor and a feature extraction based neural net training algorithm. The parallel optical processor provides high speed and vast parallelism as well as full shift invariance. The neural network algorithm enables simultaneous discrimination of multiple noisy targets in spite of their scales, rotations, perspectives, and various deformations. This fully developed OPRNN system can be effectively utilized for the automated spacecraft recognition and tracking that will lead to success in the Automated Rendezvous and Capture (AR&C) of the unmanned Cargo Transfer Vehicle (CTV). One of the most powerful optical parallel processors for automatic target recognition is the multichannel correlator. With the inherent advantages of parallel processing capability and shift invariance, multiple objects can be simultaneously recognized and tracked using this multichannel correlator. This target tracking capability can be greatly enhanced by utilizing a powerful feature extraction based neural network training algorithm such as the neocognitron. The OPRNN, currently under investigation at JPL, is constructed with an optical multichannel correlator where holographic filters have been prepared using the neocognitron training algorithm. The computation speed of the neocognitron-type OPRNN is up to 10(exp 14) analog connections/sec that enabling the OPRNN to outperform its state-of-the-art electronics counterpart by at least two orders of magnitude.

Chao, Tien-Hsin↗

NASA NTRS1993

Study of auroral dynamics with combined spacecraft and incoherent-scatter radar data

We have examined Sondrestrom incoherent-scatter radar observations of ionospheric plasma density and temperature distributions, as well as measurements of F-region ion drifts that were made during a prenoon pass by the DMSP-F7 satellite through the radar field of view. The spacecraft traversed a region of intense electron precipitation with a characteristic energy below approximately 200 eV. Particles with such low characteristic energies are believed to originate, either directly or indirectly, in the magnetosheath. The precipitation region had a width of about 2 deg invariant latitude. The corotating radar observed a patch of enhanced electron density and elevated electron temperature in the F2 region between about 10.5 and 12 magnetic local time in the same invariant latitude range where DMSP-F7 detected the soft-electron flux. The ion drift pattern, also obtained by radar, shows that it is unlikely that the plasma patch was produced by solar radiation and advected into the radar field of view. We suggest that the radar observed modifications of the ionospheric plasma distribution, which resulted from direct entry of magnetosheath electrons into the magnetosphere and down to ionospheric altitudes. Model calculations of the ionospheric response to the observed electron flux support our interpretation.

Watermann, Juergen↗

NASA NTRS1993

Attitude stabilization of a rigid spacecraft using gas jet actuators operating in a failure mode

The attitude stabilization of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes is considered. First, the case where the uncontrolled principal axis of the spacecraft is not an axis of symmetry is considered. In this case, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback. A discontinuous stabilizing feedback control strategy is constructed which stabilizes the spacecraft to an equilibrium attitude. Next, the case where the uncontrolled principal axis of the spacecraft is an axis of symmetry is considered. In this case, the complete spacecraft dynamics are not even accessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback, but again a discontinuous stabilizing feedback control strategy is constructed. In both cases, the discontinuous feedback controllers are constructed by switching between one of several feedback functions.

Krishnan, Hariharan↗

NASA NTRS1992

Energetic ion phase space densities in Neptune's magnetosphere

Ion phase densities of Neptune are presently ascertained at the first and second adiabatic invariants of charged-particle motion on the basis of an analysis of Voyager 2 measurements. The profiles thus obtained are interpreted as indicative of generally inward radial diffusion, with an energetic ion source near L = 10. Excellent agreement is obtained between inbound and outbound phase-space density profiles at the values of the invariants; this suggests approximately axisymmetric, quasi-stationary radiation belts. The inward diffusing power carried by energetic ions appears adequate for powering Neptune's aurora, if enough of the ions are lost to the Neptune atmosphere.

Cheng, Andrew F.↗

NASA NTRS1992

On slowly varying systems - l-infinity to l-infinity performance and implications to robust adaptive control

The authors present a result on the l-infinity to l-infinity performance of slowly time varying systems. In particular, it is shown that the performance of such systems cannot be much worse than that of the frozen-time systems which are time invariant. This result is used to characterize a class of indirect adaptive controllers that can stabilize a time-invariant system subjected to both parametric and l-infinity to l-infinity bounded unstructured uncertainty. Pertaining to this class of controllers, a particular indirect adaptive scheme is proposed that provides the greatest upper bound on the size of the unstructured uncertainty for which stability is ensured.

Voulgaris, Petros G.↗

NASA NTRS1992

Optical pattern recognition III; Proceedings of the Meeting, Orlando, FL, Apr. 21, 22, 1992

Consideration is given to transitioning of optical processing into systems (TOPS), optical correlator hardware, phase-only optical correlation filters, optical distortion-invariant correlation filters, and optical neural networks. Particular attention is given to a test target for optical correlators, a TOPS electronic warfare channelizer program, a portable video-rate optical correlator, a joint transform correlator employing electron trapping materials, a novelty filtered optical correlator using a photorefractive crystal, a comparison of correlation performance of smart ternary phase-amplitude filters with gray-scale and binary input scenes, real-time distortion-tolerant composite filters for automatic target identification, landscaping the correlation surface, fast designing of a circular harmonic filter using simulated annealing, feature-based correlation filters for distortion invariance, automatic target recognition using a feature-based optical neural network, and a holographic inner-product processor for pattern recognition.

Casasent, David P.↗

NASA NTRS1993

Coarse-coded higher-order neural networks for PSRI object recognition

A higher-order neural network (HONN) can be designed to be invariant to changes in scale, translation, and inplane rotation. Invariances are built directly into the architecture of a HONN and do not need to be learned. Consequently, fewer training passes and a smaller training set are required to learn to distinguish between objects. The size of the input field is limited, however, because of the memory required for the large number of interconnections in a fully connected HONN. By coarse coding the input image, the input field size can be increased to allow the larger input scenes required for practical object recognition problems. We describe a coarse coding technique and present simulation results illustrating its usefulness and its limitations. Our simulations show that a third-order neural network can be trained to distinguish between two objects in a 4096 x 4096 pixel input field independent of transformations in translation, in-plane rotation, and scale in less than ten passes through the training set. Furthermore, we empirically determine the limits of the coarse coding technique in the object recognition domain.

Spirkovska, Lilly↗

NASA NTRS1993

Three-dimensional object recognition using similar triangles and decision trees

A system, TRIDEC, that is capable of distinguishing between a set of objects despite changes in the objects' positions in the input field, their size, or their rotational orientation in 3D space is described. TRIDEC combines very simple yet effective features with the classification capabilities of inductive decision tree methods. The feature vector is a list of all similar triangles defined by connecting all combinations of three pixels in a coarse coded 127 x 127 pixel input field. The classification is accomplished by building a decision tree using the information provided from a limited number of translated, scaled, and rotated samples. Simulation results are presented which show that TRIDEC achieves 94 percent recognition accuracy in the 2D invariant object recognition domain and 98 percent recognition accuracy in the 3D invariant object recognition domain after training on only a small sample of transformed views of the objects.

Spirkovska, Lilly↗

NASA NTRS1994

Optical-Correlator Neural Network Based On Neocognitron

Multichannel optical correlator implements shift-invariant, high-discrimination pattern-recognizing neural network based on paradigm of neocognitron. Selected as basic building block of this neural network because invariance under shifts is inherent advantage of Fourier optics included in optical correlators in general. Neocognitron is conceptual electronic neural-network model for recognition of visual patterns. Multilayer processing achieved by iteratively feeding back output of feature correlator to input spatial light modulator and updating Fourier filters. Neural network trained by use of characteristic features extracted from target images. Multichannel implementation enables parallel processing of large number of selected features.

Chao, Tien-Hsin↗

NASA NTRS1992

A study of the fine scale motions of incompressible time-developing mixing layers

This work is an extension of a project conducted at the previous CTR summer program and was reported by Chen et al. (1990). In that program, the geometry and topology of the dissipating motions in a variety of shear flows was examined. All data was produced by direct numerical simulations (DNS). The partial derivatives of the velocity field were determined at every grid point in the flow and various invariants and related quantities were computed from the velocity gradient tensor. Motions characterized by high rates of kinetic energy dissipation and high enstrophy were of particular interest. Scatter diagrams of the invariants were mapped out and interesting and unexpected patterns were seen. Each type of shear layer produced its own characteristic scatter plot. In the present project, attention is focused on the incompressible plane mixing layer, and the scatter diagrams are replaced with more useful joint probability density contours. Comparison of the topology of the dissipating motions of flows at different Reynolds numbers are made. Also, plane mixing layers at the same Reynolds number but with different initial conditions are compared.

Soria, J.↗

NASA NTRS1994

Performance evaluation of digital phase-locked loops for advanced deep space transponders

The performances of the digital phase-locked loops (DPLL's) for the advanced deep-space transponders (ADT's) are investigated. DPLL's considered in this article are derived from the analog phase-locked loop, which is currently employed by the NASA standard deep space transponder, using S-domain to Z-domain mapping techniques. Three mappings are used to develop digital approximations of the standard deep space analog phase-locked loop, namely the bilinear transformation (BT), impulse invariant transformation (IIT), and step invariant transformation (SIT) techniques. The performance in terms of the closed loop phase and magnitude responses, carrier tracking jitter, and response of the loop to the phase offset (the difference between in incoming phase and reference phase) is evaluated for each digital approximation. Theoretical results of the carrier tracking jitter for command-on and command-off cases are then validated by computer simulation. Both theoretical and computer simulation results show that at high sampling frequency, the DPLL's approximated by all three transformations have the same tracking jitter. However, at low sampling frequency, the digital approximation using BT outperforms the others. The minimum sampling frequency for adequate tracking performance is determined for each digital approximation of the analog loop. In addition, computer simulation shows that the DPLL developed by BT provides faster response to the phase offset than IIT and SIT.

Nguyen, T. M.↗