Application of relaxed solutions to minimum sensitivity optimal control

Relaxed variational techniques are applied to a minimum sensitivity control problem. Sensitivity of a trajectory is minimized to perturbations in initial conditions. Rather than using the optimal control that does indeed exist and that satisfies the final conditions exactly, a suboptimal control is used that transfers the system from the given initial state to an arbitrary small neighborhood of the given final state, and that results in a considerably better performance than the optimal solution. The suboptimal control is constructed using the optimal controls of the relaxed problem.This paper is based upon the Ph.D. dissertation by the author at Purdue University, Lafayette, Indiana. The author wishes to thank Professor Violet B. Haas, School of Electrical Engineering, Purdue University, for introducing him to relaxed variational problems and for many very helpful suggestions through the course of this work.     

On observing the states of uncertain dynamical systems

For the implementation of a stable asymptotic reduced-order Luenberger observer, which is not sensitive to unknown disturbances entering the system, it is shown that specific columns of the measurement matrixC must be different from zero.This research was supported by the Technion VPR Fund, L. Rogow Aeronautical Research Fund.The author wishes to thank E. P. Ryan, G. Leitmann, and S. Gutman for helpful discussions.     

Channel simulation and coding with side information

Studies the minimum random bit rate required to simulate a random system (channel), where the simulator operates with a given external input. As measures of simulation accuracy the authors use both the variational distance and the d¯ distance between joint input-output distributions. They find the asymptotic number of random bits per input sample required for accurate simulation, as a function of the distribution of the input process. These results hold for arbitrary channels and input processes, including nonstationary and nonergodic processes and do not hinge on a specific simulation scheme. A by-product of the analysis is a general formula for the minimal achievable source coding rate with side information     

Microwave imaging of aircraft

Three methods of imaging aircraft from the ground with microwave radar with quality suitable for aircraft target recognition are described. The imaging methods are based on a self-calibration procedure called adaptive beamforming that compensates for the severe geometric distortion inherent in any imaging system that is large enough to achieve the high angular resolution necessary for two-dimensional target imaging. The signal processing algorithm is described and X-band (3-cm)-wavelength experiments demonstrate its success on commercial aircraft flying into Philadelphia International Airport.<>     

Riccati equations and Lie series

Lie series and a special matrix notation for first-order differential operators are used to show that the Lie group properties of matrix Riccati equations arise in a natural way. The Lie series notation makes it evident that the solutions of a matrix Riccati equation are curves in a group of nonlinear transformations that is a generalization of the linear fractional transformations familiar from the classical complex analysis. It is easy to obtain a linear representation of the Lie algebra of the nonlinear group of transformations and then this linearization leads directly to the standard linearization of the matrix Riccati equations. We note that the matrix Riccati equations considered here are of the general rectangular type.     

Nonlinear effects in the convective instability of a binary mixture in a porous medium near threshold

An amplitude equation is derived near threshold for both the stationary and the oscillatory instabilities and an oscillatory behavior in time for the Nusselt and the Froude number is predicted for the oscillatory instability.     

13C NMR spectra of diazastilbenes. II—Torsion angles of trans-pyridinalanilines and trans-benzylideneaminopyridines

The torsion angles of trans-pyridinalanilines and trans-benzylideneanilines were derived from the chemical shifts of the para-carbon atoms. The N-torsion angle is between 33 and 59°. For the C-torsion angle, a value of approximately 10° is obtained for the benzylideneaminopyridines and the C-torsion angle for the pyridinalalines is estimated to be in the same range.