In this study, a robust H_2/H_∞ Multi-objective state-feedback controller and tracking design are presented for a mobile two-wheeled inverted pendulum (MTWIP). The proposed control has to track the desired angular velocity while keeping the mobile two-wheeled inverted pendulum balanced. First, error of output states are added to the dynamic of system for better tracking control. And uncertainties of parameters are defined by affine parameters. Next, Takagi-Sugeno (T-S) fuzzy model is used for estimating the uncertainty of nonlinear model parameters. Robust H_2/H_∞ controller is designed and analyzed for each local linear subsystem of mobile two-wheeled inverted pendulum by using a linear matrix inequalities method. To sum up, in order to calculate the whole dynamic of system from each local linear subsystem, weight average defuzzifer method is used and the total controller is designed and analyzed according to parallel distribute compensation. The simulation indicate that the proposed scheme has high accuracy, robustness, good tracking, fast transient responses and lower control effort for a mobile two-wheeled inverted pendulum despite the uncertainties and external disturbance.

In recent years much research has been conducted to study the variations in welding parameters and consumables on the mechanical properties of steels to optimize weld integrity. The quality of weld is a very important working aspect for the manufacturing and construction industries. In the present work, an attempt has been made to apply an efficient technique, fuzzy based desirability method to solve correlated Multiple response optimization problems, in the field of flux cored arc welding. This approach converts the complex Multiple objectives into a single fuzzy reasoning grade. Based on fuzzy reasoning grade, optimum levels of parameters (Welding current, arc voltage and electrode stickout) were identified. Experiments were performed based on Taguchi method. Weld bead hardness and material deposition rate are selected as quality targets. Significant contributions of parameters are estimated using Analysis of Variance (ANOVA). Confirmation test is conducted and reported. It is found that the electrode stickout is the most significant controlled factor for the process according to the weighted fuzzy reasoning grade of the maximum weld bead hardness and material deposition rate. The proposed technique allows manufacturers to develop intelligent manufacturing system to achieve the highest level of automation.

Radial Basis function Neural Network (RBFNN) is a type of artificial neural networks used for supervised learning. They rely on radial basis functions (RBFs), nonlinear mathematical functions employed to approximate complex nonlinear data. Determining the architecture of the network is challenging, impacting the achievement of optimal learning and generalization capacities. This paper presents a Multi--objective model for optimizing and training RBFNN architecture. The model aims to fulfill three objectives: the first is the summation of distances between the input vector and the corresponding center for the neurons in the hidden layer. The second objective is the global error of the RBFNN, defined as the discrepancy between the calculated output and the desired output. The third objective is the complexity of the RBFNN, quantified by the number of neurons in the hidden layer. This innovative approach utilizes Multiple objective simulated annealing to identify optimal parameters and hyperparameters for neural networks. The numerical results provide accuracy and reliability of the theoretical results discussed in this paper, as well as advantages of the proposed approach.

Multi-hole orifices have better performance than single-hole orifices. In this paper, Multi-objective optimization of Multi-hole orifices is performed using a Fluid-Solid Interaction (FSI) analysis and Multi-objective genetic algorithm (NSGA II). In all numerical analysis, the governing equations of the solid and the governing equations of the fluid are carried out for orifice and fluid around orifice respectively. All calculations are made for a 16-hole orifice with circular holes. The design variable in the optimization process is the distance between the holes of the orifice and thus the amount of shrinkage or expansion of the orifice geometry. The objective functions are the pressure drop created on the sides of the orifice, the deformation and tension created in the orifice structure, which should be maximized, minimized and minimized respectively. In the results section, the Pareto front are presented which represent useful information for designing the Multi-hole orifices geometry, and five orifices are also introduced as final design options that have better performance. The results of the sensitivity analysis of the various parameters are also presented and discussed in detail in the Multi-hole orifices.

Since most real-world decision problems, because of incomplete information or the existence of linguistic information in the data, are including uncertainties, stochastic programming and fuzzy programming as two conventional approaches to such issues have been raised. Stochastic programming deals with optimization problems where some or all the parameters are random. In this paper, a method is provided for solving Multi-objective stochastic programming where the unknown parameters have been considered as normal random variables. In this model, it is assumed that the parameters are specified by the relevant professionals. Since there are not enough ways to solve such problems directly, the corresponding model using chance-constraint approaches, are converted to a certain Multi-objective problem. Then, a fuzzy programming technique for solving the certain Multi-objective model will be utilized. In this paper, the hyperbolic membership function is used. The final method can be solved by standard methods of nonlinear programming. Finally, numerical examples are provided to illustrate the operation of the proposed method.

An optimization model with a Multi objective function subject to a system of fuzzy relation equations with Yager’s union operator is presented. The solution set of such a fuzzy relation equations is a non-convex set. Thus, the ordinary methods such as simplex or interior point methods don't use for solving these problems. In this paper, we first characterize the feasible solution set and then, optimize a linear objective function. In order to optimize it, we convert it to an equivalent problem involving 0-1 integer programming with a branch-and-bound solution technique. Finally, we optimize a Multi objective function with LP metric methods. Furthermore, a concrete example is included for illustration purpose.