A solving tool for fuzzy quadratic optimal control problems

In this paper we propose an iterative method to solve an optimal control problem, with fuzzy target and constraints. The algorithm is developed in such a way as to satisfy the target function and the constraints. The algorithm can be applied only if a method exists to solve a crisp parametric sub-problem obtained by the original one. This is the case for a quadratic-linear target function with linear constraints, for which some well established solvable methods exist for the crisp associated sub-problem. A numerical test confirmed the good convergence properties.fuzzy, mathematical programming

Approximating a similarity matrix by a latent class model: A reappraisal of additive fuzzy clustering

Let Q be a given n×n square symmetric matrix of nonnegative elements between 0 and 1, similarities. Fuzzy clustering results in fuzzy assignment of individuals to K clusters. In additive fuzzy clustering, the n×K fuzzy memberships matrix P is found by least-squares approximation of the off-diagonal elements of Q by inner products of rows of P. By contrast, kernelized fuzzy c-means is not least-squares and requires an additional fuzziness parameter. The aim is to popularize additive fuzzy clustering by interpreting it as a latent class model, whereby the elements of Q are modeled as the probability that two individuals share the same class on the basis of the assignment probability matrix P. Two new algorithms are provided, a brute force genetic algorithm (differential evolution) and an iterative row-wise quadratic programming algorithm of which the latter is the more effective. Simulations showed that (1) the method usually has a unique solution, except in special cases, (2) both algorithms reached this solution from random restarts and (3) the number of clusters can be well estimated by AIC. Additive fuzzy clustering is computationally efficient and combines attractive features of both the vector model and the cluster mode

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems

This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA–PS–SQP algorithm is very efficient in solving power system economic dispatch problem

Brain image clustering by wavelet energy and CBSSO optimization algorithm

Previously, the diagnosis of brain abnormality was significantly important in the saving of social and hospital resources. Wavelet energy is known as an effective feature detection which has great efficiency in different utilities. This paper suggests a new method based on wavelet energy to automatically classify magnetic resonance imaging (MRI) brain images into two groups (normal and abnormal), utilizing support vector machine (SVM) classification based on chaotic binary shark smell optimization (CBSSO) to optimize the SVM weights. The results of the suggested CBSSO-based KSVM are compared favorably to several other methods in terms of better sensitivity and authenticity. The proposed CAD system can additionally be utilized to categorize the images with various pathological conditions, types, and illness modes

Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements