Using an optically-controlled phase spatiallight modulator (SLM) instead of the fixed phase-shifting dot, we havesimulated and experimentally demonstrated a nonlinear Zernike filterrobust to wavefront tilt misalignments. In the experiments, a liquid-crystal light valve (LCLV) was used as the phase SLM. The terminology "nonlinear" Zernike filter refers to the nonlinear filteringoperation that takes place in the Fourier domain due to the phase changefor field spectral components being proportional to the spectral componentintensities.

Because the Zernike filter output intensity is directlyrelated to input wavefront phase, a parallel, distributed feedback systemcan replace the wavefront reconstruction calculations normally requiredin adaptive-optic phase correction systems. Applications include high-resolution phase distortion suppression for atmospheric turbulence,optical phase microscopy, and compensation of aberrations in optical system components.

A factor of eight improvement in Strehl ratio wasobtained experimentally, and simulation results suggest that even betterperformance could be obtained by replacing the LCLV with a more sophisticated optically-controlled phase SLM.

(This work to appear in Proc. 1999 American Control Conference.)

A hierarchical algorithm using multipole approximation speeds up the evaluation of the demagnetizing field, reducing computational cost from O(N^2) to O(NlogN). A hybrid 3D/1D rod model is adopted to compute the magnetostriction: a 3D model is used in solving the LLG equation for the dynamics of magnetization; then assuming that the rod is along z-direction, we take all cells with same z-cordinate as a new cell. The values of the magnetization and the effective field of the new cell are obtained from averaging those of the original cells that the new cell contains. Each new cell is represented as a mass-spring in solving the motion equation.

Numerical results include: 1. domain wall dynamics, including domain wall formation and motion; 2. effects of physical parameters, grid geometry, grid refinement and field step on H-M hysteresis curves; 3. magnetostriction curve.

First, we consider the problem of computing the controllability energyfunction without numerically solving the family of optimal control problems,or the associated Hamilton-Jacobi-Bellman equation, implied in its definition.Stochastically excited systems play a major role in our methodology. Wepresent a stochastic method for computing an estimate of the controllabilityfunction, and show that in certain situations the method provides an exactsolution. The procedure is tested on applications via Monte-Carlo experiments.

Then, we address the problem of numerically determining a Morse transformationfor a function with non-degenerate critical point at 0. We develop analgorithm for computing the desired nonlinear transformation and estimatingthe neighborhood on which the transformed controllability function isquadratic.

In the literature, examples of applied nonlinear balancing have been limited topseudo-balancing of 2-dimensional gradient systems and noting that in the caseof linear systems the energy functions approach reduces to the usual setting ofgramians. We apply our approach to numerically derive, for the first time,balanced representations of nonlinear state-space models. In particular, wepresent applications to a forced damped pendulum system and a forced dampeddouble pendulum system.

We utilize the low-dimensional model for the magnetostrictive actuator that was developed in earlier work. For low frequency inputs, the model approximates to a rate-independent hysteresis operator, with current as its input and magnetization as its output. Magnetostrictive strain is proportional to the square of the magnetization. In this paper, we use a classical Preisach operator for the rate-independent hysteresis operator.

We present the results of experiments conducted on a commercial magnetostrictive actuator, the purpose of which was the control of the displacement/strain output. A constrained least-squares algorithm is employedto identify a discrete approximation to the Preisach measure. We then discussa nonlinear inversion algorithm for the resulting Preisach operator, basedon the theory of strictly-increasing operators. This algorithm yields a control input signal to produce a desired magnetostrictive response.

The effectiveness of the inversion scheme is demonstrated via an open-looptrajectory tracking experiment.