Diah Chaerani

The robust optimization based Model Predictive Control using box uncertainty set

The paper considers the application of Robust Optimization (RO) to Model Predictive Control (MPC). This optimization methodology incorporates the uncertain data, which means the data of an optimization problem is not known exactly at the time when its solution has to be determined. The robust optimization has been expanded and applied to various kinds of application, in this paper, it is shown the application in MPC. The RO based MPC is simulated to a waste heat boiler control.

Fractional Differential Equation as a Models of Newton Fluids for Stress and Strain Problems

An ordinary differential equation is a branch of mathematics that is always interesting to be learned and developed due to its numerous variations in both the theory and its application. In general, the most discussed differential equation is the ordinary differential equation that has the natural number as its order. However, currently, the order of a differential equation which has been developed into a fractional-order (i.e. rational numbers) is also very interesting to be studied. This paper presents a study of ordinary differential equations that has fractional order, in which the left side contains two derivative functions with fractional order while the right side contains polynomial function n degree. Specifically, this paper presents the general form of equations, methods of finding the solution in three cases, and its application. Solutions are proposed using the Laplace transformation and its inverse and are expressed in the form of Mittag-Lefler function. Its graph is also later described using Matlab. Results of this research are expressed by three functions of three different theoretical cases and a solution to an application problem. Additionally, the study has also shown that the convergence of a number sequence of fractional differential equation order is positively related to the convergence of solution function sequence. There are many applications of fractional differential equations in the field of viscoelasticity. Therefore, at the end of the paper, this application is presented particularly regarding the relationship between stress and strain for solids and for Newtonian fluids. Keywords— Fractional Differential equations, Mittag-Lefler, stress, Strain

The convergence of the order sequence and the solution function sequence on fractional partial differential equation

One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

Hardware in the loop simulation of railway traffic re-scheduling by means of MILP algorithm

The paper considers hardware in the loop simulation (HILS) of railway traffic re-scheduling during disturbances. The traffic re-scheduling during disturbances is formulated as a mixed integer linear programming (MILP) solved by using branch and bound algorithm. The HILS apparatus is then set-up to verify the results.