Abstract: This paper is concerned with a system of
Hamilton-Jacobi-Bellman equations coupled with an autonomous
dynamical system. The mathematical system arises in the differential
game formulation of political economy models as an infinite-horizon
continuous-time differential game with discounted instantaneous
payoff rates and continuously and discretely varying state variables.
The existence of a weak solution of the PDE system is proven and
a computational scheme of approximate solution is developed for a
class of such systems. A model of democratization is mathematically
analyzed as an illustration of application.
Abstract: Conditions corresponding to the unconditional stability
of convection in a mechanically anisotropic fluid saturated porous
medium of infinite horizontal extent are determined. The medium
is heated from below and its bounding surfaces are subjected to
temperature modulation which consists of a steady part and a
time periodic oscillating part. The Brinkman model is employed
in the momentum equation with the Bousinessq approximation.
The stability region is found for arbitrary values of modulational
frequency and amplitude using the energy method. Higher order
numerical computations are carried out to find critical boundaries
and subcritical instability regions more accurately.
Abstract: In this paper, we present a model and an algorithm for
the calculation of the optimal control limit, average cost, sample size,
and the sampling interval for an optimal Bayesian chart to control
the proportion of defective items produced using a semi-Markov
decision process approach. Traditional p-chart has been widely
used for controlling the proportion of defectives in various kinds
of production processes for many years. It is well known that
traditional non-Bayesian charts are not optimal, but very few optimal
Bayesian control charts have been developed in the literature, mostly
considering finite horizon. The objective of this paper is to develop
a fast computational algorithm to obtain the optimal parameters of a
Bayesian p-chart. The decision problem is formulated in the partially
observable framework and the developed algorithm is illustrated by
a numerical example.
Abstract: The problem of lot sizing, sequencing and scheduling
multiple products in flow line production systems has been studied
by several authors. Almost all of the researches in this area assumed
that setup times and costs are sequence –independent even though
sequence dependent setups are common in practice. In this paper we
present a new mixed integer non linear program (MINLP) and a
heuristic method to solve the problem in sequence dependent case.
Furthermore, a genetic algorithm has been developed which applies
this constructive heuristic to generate initial population. These two
proposed solution methods are compared on randomly generated
problems. Computational results show a clear superiority of our
proposed GA for majority of the test problems.
Abstract: In this paper, a nonlinear model predictive swing-up
and stabilizing sliding controller is proposed for an inverted
pendulum-cart system. In the swing up phase, the nonlinear model
predictive control is formulated as a nonlinear programming problem
with energy based objective function. By solving this problem at
each sampling instant, a sequence of control inputs that optimize the
nonlinear objective function subject to various constraints over a
finite horizon are obtained. Then, this control drives the pendulum to
a predefined neighborhood of the upper equilibrium point, at where
sliding mode based model predictive control is used to stabilize the
systems with the specified constraints. It is shown by the simulations
that, due to the way of formulating the problem, short horizon
lengths are sufficient for attaining the swing up goal.