Optimum control of purpose activities in the area of quality based on a linear model of dynamics in state space

The paper considers the optimization problem formulation at goal-setting in the field of quality on the basis of a dynamics verified linear model in the state space using stepwise and linear laws of enterprise activity management. The classical quadratic functional to find optimal solutions for goal-setting was used. The direct connection of these functional components with the Taguchi loss function for product quality indicators has been substantiated, and the function scope application on the managing purposeful activities process has been expanded. The optimization parameters are determined, which are the amplification factors of the control actions. These actions ensure the actual attainability of the set goals in the field of quality during the time planned period. The optimal solutions search was carried out on the example of the textile and light industry CJSC “Salyut” (St. Petersburg). The functional minimum value in case of stepwise control law is more than 14 times greater than with a linear law. This fact found under the condition of equal unit costs for quality losses and control caused by their deviations from the nominal values. The results obtained can be used for a reasonable choice of the enterprise management law in the goal-setting in the field of quality.

Ulam Stabilities and Instabilities of Euler–Lagrange-Rassias Quadratic Functional Equation in Non-Archimedean IFN spaces

In this paper, we use direct and fixed-point techniques to examine the generalised Ulam–Hyers stability results of the general Euler–Lagrange quadratic mapping in non-Archimedean IFN spaces (briefly, non-Archimedean Intuitionistic Fuzzy Normed spaces) over a field.

Position-dependent mass Dirac equation and local Fermi velocity

We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.

Optimal control of the blowing mode parameters during basic oxygen furnace steelmaking process

The oxygen converter is intended for production of steel from liquid cast iron and steel scrap at blowing by oxygen. Nowadays, Basic Oxygen Furnace process is the main method for steelmaking. The main disadvantage of the basic oxygen furnace is the limited ability to increase the part of scrap metal. The task of the proposed approach is to control of the blowing mode parameters to establish the optimal level of CO2 that will ensure a minimum specific cost of steel in the presence of restrictions and boundary conditions of basic oxygen furnace steelmaking process. A model predictive control taking into account the constraints on the input signals and the quadratic functional is proposed. The design of Model Predictive Control is based on mathematical model of an object. This approach minimizes the cost function that characterizes the quality of the process. The result of the automatic control system modeling shows that the Model Predictive Control approach provides retention of carbon dioxide level when oxygen consumption is changing. The obtained quadratic functional is optimized to find the optimal control of blowing parameters.

Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.

Algorithm for Finding Feedback in a Problem with Constraints for One Class of Nonlinear Control Systems

For a continuous nonlinear control system on a finite time interval with control constraints, where the right-hand side of the dynamics equations is linear in control and linearizable in the vicinity of the zero equilibrium position, we consider the construction of a feedback according to the Kalman algorithm. For this, the solution of an auxiliary optimal control problem with a quadratic functional is used by analogy with the SDRE approach.Since this approach is used in the literature to find suboptimal synthesis in optimal control problems with a quadratic functional with formally linear systems, where all coefficient matrices in differential equations and criteria can contain state variables, then on a finite time interval it becomes necessary to solve a complicated matrix differential Riccati equations, with state-dependent coefficient matrices. This circumstance, due to the nonlinearity of the system, in comparison with the Kalman algorithm for linear-quadratic problems, significantly increases the number of calculations for obtaining the coefficients of the gain matrix in the feedback and for obtaining synthesis with a given accuracy. The proposed synthesis construction algorithm is constructed using the extension principle proposed by V. F. Krotov and developed by V. I. Gurman and allows not only to expand the scope of the SDRE approach to nonlinear control problems with control constraints in the form of closed inequalities, but also to propose a more efficient computational algorithm for finding the matrix of feedback gains in control problems on a finite interval. The article establishes the correctness of the application of the extension principle by introducing analogs of the Lagrange multipliers, depending on the state and time, and also derives a formula for the suboptimal value of the quality criterion. The presented theoretical results are illustrated by calculating suboptimal feedbacks in the problems of managing three-sector economic systems.

The control optimization algorithm for automatic braking of a wheeled vehicle

Introduction (problem statement and relevance). One of the most promising and intensively developing directions in the automation field of road transport management is the creation of highly automated vehicles.The purpose of the study was to find a way to solve a wheeled vehicle safe automatic braking problem in terms of minimizing quality control of the quadratic functional and work out optimal software and hardware implementation of this system.Methodology and research methods. To solve the problem, the method of the control algorithm analytical design was used, basing on the use of the necessary conditions for minimizing the elements of the functional for the control law synthesis. The maximum deceleration value was due to the identified tire grip, and the deceleration threshold from which braking begins was selected as the minimum of the working deceleration and two decelerations depending on the rear obstacle distance.Scientific novelty and results. The tests of the developed function were carried out for the LADA Vesta vehicle equipped with an ABS valve body with the possibility of programmed control. The analysis of the research results showed that when solving the problem of safe automatic braking in front of an obstacle, the software limitation of braking deceleration did not allow wheel blocking and performed the functions of an anti-lock braking system at the permissible wheel slipping level; software backup of the distance calculation to the front obstacle from the moment of braking start allowed to prevent most of the situations with false data from the radar when the vehicle pecked during braking.Practical significance. Software tuning of mathematical models parameters of the engine, transmission and braking system allows you to adapt the automatic braking system to a wide class of vehicle models.

Functional inequalities for generalized multi-quadratic mappings

In this article, we introduce some special several variables mappings which are quadratic in each variable and show that such mappings can be defined as a single equation that is the generalized multi-quadratic functional equation. We also apply a fixed point theorem to establish the Hyers–Ulam stability for the generalized multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to some known stability results.

Characterization and stability analysis of advanced multi-quadratic functional equations

In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigate n-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.

General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space

The investigation of the stabilities of various types of equations is an interesting and evolving research area in the field of mathematical analysis. Recently, there are many research papers published on this topic, especially additive, quadratic, cubic, and mixed type functional equations. We propose a new functional equation in this study which is quite different from the functional equations already dealt in the literature. The main feature of the equation dealt in this study is that it has three different solutions, namely, additive, quadratic, and mixed type functions. We also prove that the stability results hold good for this equation in intuitionistic random normed space (briefly, IRN-space).