The problem of optimal control of the equilibrium states of the Lorenz system in both finite and infinite time intervals has been studied. The optimal control functions ensuring asymptotic stability of desired states in both cases are obtained as functions of the phase state and time. The squared Euclidean norm of the perturbed state of the Lorenz system in both cases is obtained as transcendental function of time. As an applications, it was shown that the equilibrium states of the Lorenz system are asymptotic stable.

Optimal control of stochastic prey–predator models during infinite and finite time intervals is considered. Optimal feedback controlling functions are derived as non-linear functions of the densities of prey and predator populations using Lyapunov–Bellman technique. The densities of both prey and predator populations are obtained as functions of time. We will be concerned with time intervals of the control process and time dependence of the control functions.

This paper studied a continuous-time model of a production maintenance system in which a manufacturing firm produces a single product selling some and stocking the remaining. The problem of adaptive control of a production-maintenance system with unknown deterioration has been presented. Using Liapunov technique, the production rate and updating rule of deterioration rate are derived as non-linear functions of inventory level perturbation. Numerical analysis for the system has been presented for a set of parameter values and demand rate.

A production process whose performance deteriorates over time is studied in this paper. It is assumed that the process performance can be measured in terms of the proportion of good units of end items produced. Using the pontryagin principle, the optimal scheduled production rate and preventive maintenance rate will be derived as a function of both production rate and proportion of good units. The controlled system can be modeled by a system of non-linear differential equations and its solution will be discussed numerically.

This paper deals with a continuous-time model of a production and maintenance system whose performance

deteriorates over time. The problem of adaptive control of a production-maintenance system with unknown

deterioration rate is presented. Using a feedback the scheduled production rate, preventive maintenance rate,

and updating rule of deterioration and obsolescence rates will be derived.

An empirical investigation is focused on the relationship between material flow patterns in a manufacturing system and the distribution of the volume distance values associated with all possible solutions to a line layout problem. Volume distance distribution for line layout problems are shown to follow roughly normal distribution for some common material flow patterns.

This study investigates the predictability of the form and parameters of the distribution of materials handling volume distance values associated with layout problems characterized by static distance functions. Previous research suggests that volume distance distributions associated with line layout problems tend toward normality. This study extends these results to more general cases of layout problems where distances between workcentre locations do not vary with alternative assignments of workcentres to locations.