Joseph L. Hibey

Singular perturbations and time scales (SPaTS) in discrete control systems-an overview

This paper presents an overview of recent developments in the theory of singular perturbations and time scales (SPaTS) in discrete control systems. The focus is in three directions: modeling, analysis, and control. First, sources of discrete models and the effect of the discretizing interval on the modeling are reviewed. Then the analysis of two-time scale systems is presented to bring out typical characteristic features of SPaTS. Finally, in the control of the two-time scale systems, the important issue of multirate sampling is addressed. The bibliography containing over 100 titles is included.

Necessary conditions for partially observed diffusions

We present a new approach to deriving necessary conditions for stochastic partially observed control problems when the control enters the drift coefficient, and correlation between signal and observation noise is allowed. The problem is formulated as one of complete information but, instead of considering the unnormalized conditional density of nonlinear filtering, using Kunitas decomposition this equation is decomposed into two measure-valued processes. The minimum principle and the stochastic partial differential equation satisfied by the adjoint process, are then derived, and are shown to be the exact necessary conditions when the correlation is zero.<<ETX>>

Application of stochastic stability theory to linear time varying systems containing interval matrices

Known conditions for the stability of stochastic, linear time varying (LTV) dynamical systems based on Lyapunov theory are applied to LTV dynamical systems containing interval matrices; both discrete and continuous time processes are considered. These conditions are sufficient for stability WPL and in the case of discrete time, also necessary for stability in MS. They lead to a simple, noninterative technique that involves the computation of eigenvalues of matrices whose elements often consist of first and/or second order moments. The results are useful in areas such as robust design, feedback control, perturbation analysis, and fault tolerant systems.<<ETX>>

Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem

The optimal control problem arising in coplanar orbital transfer using aeroassist technology is addressed. The maneuver involves the transfer from high earth orbit to low earth orbit with minimum fuel consumption. Simulations are carried out to obtain a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the present work is the application of an efficient multiple shooting method for handling the difficult nonlinear two-point boundary value problem resulting from the optimization procedure.<<ETX>>

Chaotic behavior of a marked point process

Abstract The logistic equation, a discrete-time process, is embedded in a continuous-time marked point process of the Poisson type. The concept of the Liapunov exponent used in the study of chaos is then applied to the point process to describe some of its behavior. Characterizations in terms of Markov processes and martingales are used in the analysis.

Analyzing the Chaotic Behavior of the Logistics Equation Represented as a Marked Point Process

The logistics equation, a discrete-time process, is embedded in a continous-time marked point process of the Poisson type. The concept of the Liapanov exponent used in the study of chaos is then applied to the point process to describe some of its behavior. Characterizations in terms of Markov processes and martingales are used in the analysis.

Cycle Slipping in an Optical Communication System Employing Subcarrier Angle Modulation

The output of an ideal photodetector that is modeled as a doubly stochastic Poisson Process is used to excite a phase-locked loop. The rate of this Poisson process contains an angle modulated subcarrier process that is modeled as a Gauss-Markov process. A measure transformation involving a martingale translation is applied to the suboptimal filter used to estimate the Phase. Cycle slipping is then discussed with respect to the evolution of the Phase error Process under the new measure. The approach is in the context of a first passage problem and uses a Kramers-Moyal expansion of the equation satisfied by the mean slip time. Various approximations to the jump rate and size are assumed, and a perturbation analysis results in asymototic representations of the correspondinq solutions. Comparisons with solutions obtained from so-called diffusion approximations are also included, as well as a specific example to illustrate the procedure.