Engineering topics

Zak, Michail

Publications and source records attributed to Zak, Michail.

79 records · Page 5

NASA NTRS1989

Unsupervised learning in neurodynamics using example-interaction approach

A new concept for unsupervised learning based upon examples introduced to the neural network is proposed. Each example is considered as an interpolation node of the velocity field in the phase space. The velocities at these nodes are selected such that all the streamlines diverge to an attracting set imbedded in the subspace occupied by the cluster of examples. The synaptic interconnections are found from the minimization of the strength energy, while the node velocities play the role of constraints.

Zak, Michail↗

NASA NTRS1989

Terminal attractors in neural networks

A new type of attractor (terminal attractors) for content-addressable memory, associative memory, and pattern recognition in artificial neural networks operating in continuous time is introduced. The idea of a terminal attractor is based upon a violation of the Lipschitz condition at a fixed point. As a result, the fixed point becomes a singular solution which envelopes the family of regular solutions, while each regular solution approaches such an attractor in finite time. It will be shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the synaptic weights. The applications of terminal attractors for content-addressable and associative memories, pattern recognition, self-organization, and for dynamical training are illustrated.

Zak, Michail↗

NASA NTRS1988

Terminal attractors for addressable memory in neural networks

A new type of attractors - terminal attractors - for an addressable memory in neural networks operating in continuous time is introduced. These attractors represent singular solutions of the dynamical system. They intersect (or envelope) the families of regular solutions while each regular solution approaches the terminal attractor in a finite time period. It is shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the weight matrix.

Zak, Michail↗

NASA NTRS1988

Dispersion, damping and confinement of propagating pulses in large space structures

Pulse propagations in large space structures caused by repeated pulse excitations are studied analytically (by using the Z-transforms) and numerically. It is found that resonance regimes can be generated not only by periodical, but also by non-periodical repeated pulses; the conditions for such regimes are derived. Special attention is paid to the dispersion of propagating pulses due to structural irregularities, to damping of pulses due to appropriate combination of elastic and viscous properties of joints between structural members, and to the protection of certain areas of Large Space Structures (LSS) from impacts provided by a pulse trapping effect.

Zak, Michail↗

NASA NTRS1987

Concept of adaptive structures

The concept of adaptive structures is brought up in connection with the need in ultra lightweight structural systems to maintain desired properties and configurations without human intervention when subjected to dynamic, thermal, and other environmental forces. Examples are large antenna structures and flexible robotic structures. In the both cases such adaptivity would allow less massive structural members to be employed under normal loading conditions. During special circumstances when unusually large loads are encountered, temporary stiffening would allow the use of less sturdy structures, resulting in large savings in their cost, and in increasing their mobility and efficiency. Within the framework of a finite-dimensional representation of structural dynamics, the adaptivity can be implemented by the dependence of the stiffness matrix (k) upon the expected load (Q), or expected (programmed) changes in configurations, i.e., (k) = (k(t)) where the dependence upon time is programmed in advance. In order to sustain unexpected loads the adaptive structure can be provided by feedback force control, or by a parametrical stiffness control.

Zak, Michail↗

NASA NTRS1987

Dynamical response to pulse excitations in large space structures

Finite dimensional approximations of large space structures as distributed parameter systems may lead to a loss of contribution of high frequencies to the dynamic response in case of impulsive or concentrated loads. It is shown that the unmodeled part of this response can be represented by a system of thin pulses which propagate as characteristic waves. It is demonstrated that the dynamical response to such a system of pulses can be modeled by a system of equations with delay argument. Fundamental dynamical properties of this system such as Liapunov stability, structural stability, loss of periodicity and transition to ergodicity are analyzed in this study. The results are illustrated by examples.

Zak, Michail↗

NASA NTRS1986

Closure in turbulence theory using stabilization principle

The approach presented is based upon the concept that the velocity fluctuations driven by the instability of the original flow grow until a new stable state is approached. The application of this stabilization principle is demonstrated by describing the smoothing out of a velocity discontinuity.

Zak, Michail↗