An explicit solution to the optimal LQG problem for flexible structures with collocated rate sensors

We present a class of compensators in explicit form (not requiring numerical computer calculations) for stabilizing flexible structures with collocated rate sensors. They are based on the explicit solution, valid for both Continuum and FEM Models, of the LQG problem for minimizing mean square rate. They are robust with respect to system stability (will not destabilize modes even with mismatch of parameters), can be instrumented in state space form suitable for digital controllers, and can be specified directly from the structure modes and mode 'signature' (displacement vectors at sensor locations). Some simulation results are presented for the NASA LaRC Phase-Zero Evolutionary Model - a modal Trust model with 86 modes - showing damping ratios attainable as a function of compensator design parameters and complexity

Some nonlinear damping models in flexible structures

A class of nonlinear damping models is introduced with application to flexible flight structures characterized by low damping. Approximate solutions of engineering interest are obtained for the model using the classical averaging technique of Krylov and Bogoliubov. The results should be considered preliminary pending further investigation

Application of optical distributed sensing and computation to control of large space structures

A real time holographic sensing technique is introduced and its advantages are investigated from the filtering and control point of view. A feature of holographic sensing is its capability to make distributed measurements of the position and velocity of moving objects, such as a vibrating flexible space structure. This work is based upon the distributed parameter models of linear time invariant systems, particularly including the linear oscillator equations describing the vibration of large flexible space structures. The general conclusion is that application of optical distributed sensors bring gains in the situation where Kalman filtering is necessary for state estimation. In this case, both steady state and transient filtering error covariance become smaller. This in turn results in smaller cost in the LQG problem

Noise-amplitude dependence of the invariant density for noisy, fully chaotic one-dimensional maps

We present some analytic, non-perturbative results for the invariant density rho(x) for noisy one-dimensional maps at fully developed chaos. Under periodic boundary conditions, the Fourier expansion method is used to show precisely how noise makes rho(x) absolutely continuous and smoothens it out. Simple solvable models are used to illustrate the explicit dependence of rho(x) on the amplitude eta of the noise distribution, all the way from the case of zero noise (eta > 0) to the completely noise-dominated limit (eta=1).Comment: 15 pages, 5 Postscript figures (To appear in Phys. Rev. E

Estimation of squeezing properties of multiphoton coherent states from optical tomograms

We have examined both single and entangled two-mode multiphoton coherent states and shown how the `Janus-faced' properties between two partner states are mirrored in appropriate tomograms. Entropic squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of tuning the relative phase to enhance squeezing properties of the state. Finally we have examined the manner in which decoherence affects squeezing and the changes in the optical tomogram of the state due to interaction with the environment.Comment: 18 pages, 33 figure

A survey of the state-of-the-art and focused research in range systems

In this one-year renewal of NASA Contract No. 2-304, basic research, development, and implementation in the areas of modern estimation algorithms and digital communication systems have been performed. In the first area, basic study on the conversion of general classes of practical signal processing algorithms into systolic array algorithms is considered, producing four publications. Also studied were the finite word length effects and convergence rates of lattice algorithms, producing two publications. In the second area of study, the use of efficient importance sampling simulation technique for the evaluation of digital communication system performances were studied, producing two publications