We introduce a single location periodic review inventory control problem with lost sales and fractional lead times. We model the optimal inventory control problem as a stochastic dynamic program and analyze properties of the objective function as well as the optimal policy. We present upper and lower bounds on the optimal policy. These bounds can readily be used in easily computable heuristics....

Temperature control in buildings has been a highly studied area of research and interest since it affects the comfort occupants. Commonly, temperature systems like centralized air conditioning or heating work with fixed set point locally at thermostat, but users turn on off system when they feel is too hot cold. This configuration clearly not optimal terms energy consumption even thermal for us...

We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with fractional derivatives. We then obtain, following the Lagrange multiplier technique used in (Agrawal, 2004), a new version of Noether’s theorem to fractional optima...

In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modelling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is also presented. The t...

Abstract: In this article, a mathematical model of HIV infection is developed using fractional-order differential equation consisting uninfected CD4+T cells, infected CD4+T cells and CTL effectors (i.e. immune response cells). The fractional order model possesses non-negative solutions. The system has three equilibria: infectionfree equilibrium, infected equilibrium and CTL equilibrium. Stabili...

This paper presents a general formulation and numerical scheme for Fractional Optimal Control Problem (FOCP) of a distributed system in cylindrical coordinate and uses a hollow cylinder with axial symmetry as the example to demonstrate the method. The fractional derivatives are expressed in the Caputo-Sense. The performance index of FOCP is considered as a function of both the state and the con...

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...

In order to improve the time-frequency resolutions of short-time fractional Fourier transform, adaptive short-time fractional Fourier transform (ASTFRFT) method is used in this paper. The optimal order of ASTFRFT is given by maximizing kurtosis of signals in fractional domain, where the window width of ASTFRFT is searched by the maximal Shannon entropy of timefrequency distribution. Short-time ...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...