Application of Interval Predictor Model Into Model Predictive Control

In this paper, interval prediction model is studied for model predictive control (MPC) strategy with unknown but bounded noise. After introducing the family of models and some basic information, some computational results are presented to construct interval predictor model, using linear regression structure whose regression parameters are included in a sphere parameter set. A size measure is used to scale the average amplitude of the predictor interval, then one optimal model that minimizes this size measure is efficiently computed by solving a linear programming problem. The active set approach is applied to solve the linear programming problem, and based on these optimization variables, the predictor interval of the considered model with sphere parameter set can be directly constructed. As for choosing a fixed non-negative number in our given size measure, a better choice is proposed by using the Karush-Kuhn-Tucker (KKT) optimality conditions. In order to apply interval prediction model into model predictive control, the midpoint of that interval is substituted in a quadratic optimization problem with inequality constrained condition to obtain the optimal control input. After formulating it as a standard quadratic optimization and deriving its dual form, the Gauss-Seidel algorithm is applied to solve the dual problem and convergence of Gauss-Seidel algorithm is provided too. Finally simulation examples confirm our theoretical results.

Fuzzy Multi-objective Linear Programming Problem using DM's Perspective

In this paper, a two-stage method has been proposed for solving Fuzzy Multi-objective Linear Programming Problem (FMOLPP) with Interval Type-2 Triangular Fuzzy Numbers (IT2TFNs) as its coefficients. In the first stage of problem solving, the imprecise nature of the problem has been handled. All technological coefficients given by IT2TFNs are first converted to a closed interval and then the objectives are made crisp by reducing a closed interval into a crisp number and constraints are made crisp by using the concept of acceptability index. The amount by which a specific constraint can be relaxed is decided by the decision maker and thus the problem reduces to a crisp multi-objective linear programming problem (MOLPP). In the second stage of problem solving, the multi-objective nature of the problem is handled by using fuzzy mathematical programming approach. In order to explain the methodology, two numerical examples of the proposed methodology in Production planning and Diet planning problems have also been worked out in this paper.

A new Mean Deviation and Advanced Mean Deviation Techniques to Solve Multi-Objective Fractional Programming Problem Via Point-Slopes Formula

In this paper, we have proposed a new technique to find an efficient solution to fractional programming problems (FPP). The multi-objective fractional programming problem (MOFPP) is converted into multi-objective linear programming (MOLPP) utilizing the point-slopes formula for a plane, which has equivalent weights to the MOFPP. The MOLPP is diminished to a single objective linear programming problem (SOLPP) through using two new techniques for the values of the objective function and suggesting an algorithm for its solution. Finally, we obtained the optimal solution for MOFPP by solving the consequent linear programming problem (LPP). The proposed practicability is confirmed with the existing approaches, with some numerical examples and we indicated comparison with other techniques.

Calculating Fuzzy Inverse Matrix Using Linear Programming Problem: An Improved Approach

Calculating the matrix inverse is a key point in solving linear equation system, which involves complex calculations, particularly when the matrix elements are (Left and Right) fuzzy numbers. In this paper, first, the method of Kaur and Kumar for calculating the matrix inverse is reviewed, and its disadvantages are discussed. Then, a new method is proposed to determine the inverse of fuzzy matrix based on linear programming problem. It is demonstrated that the proposed method is capable of overcoming the shortcomings of the previous matrix inverse. Numerical examples are utilized to verify the performance and applicability of the proposed method.

The k-Metric Dimension of a Unicyclic Graph

Given a connected graph G=(V(G),E(G)), a set S⊆V(G) is said to be a k-metric generator for G if any pair of different vertices in V(G) is distinguished by at least k elements of S. A metric generator of minimum cardinality among all k-metric generators is called a k-metric basis and its cardinality is the k-metric dimension of G. We initially present a linear programming problem that describes the problem of finding the k-metric dimension and a k-metric basis of a graph G. Then we conducted a study on the k-metric dimension of a unicyclic graph.