Stability and control of the nonlinear system for tractor with N trailer in the presence of slip

In many engineering systems, it is not enough to merge the system paths to zero at infinite time, but the speed of moving these paths to zero is very important. Estimating this speed can be done using exponential functions. This concept is used in exponential stability definition. The purpose of this paper is to design a controller for problem inputs and implement a system of a car with N to a trailer connected to it. This approach is based on the analysis of the Lyapunov stability method. In the given problem, the purpose of conducting and converging the system considering the slip phenomenon as a primitive uncertainty in the system is toward the desired point. Since the trailer tractor system has limitation constraints in the modeling structure, it is difficult to guarantee the stability of a non-holonomic system. Because no controller designed by the control feedback method can continuously and stable ensure the convergence of the system. If this possibility almost dynamic errors, even adaptive controls do not versatile with the operation of the Lyapunov function, especially in the presence of uncertainties, which is a very important factor in system instability, which requires the development of controllers designed to deal with these disturbances. In the simulated results, this paper not only examines the convergence properties, but also shows the ability to control the system by designing a controller in the presence of a slip phenomenon to strengthen the system in the stability debate.

Existence and Stability of a Caputo Variable-Order Boundary Value Problem

In this study, we investigate the existence of a solution to the boundary value problem (BVP) of variable-order Caputo-type fractional differential equation by converting it into an equivalent standard Caputo (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All our results in this study are proved by using Darbo’s fixed-point theorem and the Ulam–Hyers (UH) stability definition. A numerical example is given at the end to support and validate the potentiality of our obtained results.

On the new Hyers–Ulam–Rassias stability of the generalized cubic set-valued mapping in the incomplete normed spaces

We present a novel generalization of the Hyers–Ulam–Rassias stability definition to study a generalized cubic set-valued mapping in normed spaces. In order to achieve our goals, we have applied a brand new fixed point alternative. Meanwhile, we have obtained a practicable example demonstrating the stability of a cubic mapping that is not defined as stable according to the previously applied methods and procedures.

Self-organization and control of structural-phase transformations of materials for engineering product quality assurance

The analysis of structures self-organization at intensive complex technological impacts by means of the separation of order parameters at material cooling and product discharge with the mode stability definition in a thermo-dynamic system state is carried out. There are offered ways for the intensification of structure formation processes at material processing and structure stabilization realizing the combination of control parameters of pressure and thermal impacts.

Controlled School Choice with Soft Bounds and Overlapping Types

School choice programs are implemented to give students/parents an opportunity to choose the public school the students attend. Controlled school choice programs need to provide choices for students/parents while maintaining distributional constraints on the composition of students, typically in terms of socioeconomic status. Previous works show that setting soft-bounds, which flexibly change the priorities of students based on their types, is more appropriate than setting hard-bounds, which strictly limit the number of accepted students for each type. We consider a case where soft-bounds are imposed and one student can belong to multiple types, e.g., “financially-distressed” and “minority” types. We first show that when we apply a model that is a straightforward extension of an existing model for disjoint types, there is a chance that no stable matching exists. Thus we propose an alternative model and an alternative stability definition, where a school has reserved seats for each type. We show that a stable matching is guaranteed to exist in this model and develop a mechanism called Deferred Acceptance for Overlapping Types (DA-OT). The DA-OT mechanism is strategy-proof and obtains the student-optimal matching within all stable matchings. Furthermore, we introduce an extended model that can handle both type-specific ceilings and floors and propose a extended mechanism DA-OT* to handle the extended model. Computer simulation results illustrate that DA-OT outperforms an artificial cap mechanism where we set a hard-bound for each type in each school. DA-OT* can achieve stability in the extended model without sacrificing students’ welfare.

Explicit and Implicit Cosimulation Methods: Stability and Convergence Analysis for Different Solver Coupling Approaches

The numerical stability and the convergence behavior of cosimulation methods are analyzed in this manuscript. We investigate explicit and implicit coupling schemes with different approximation orders and discuss three decomposition techniques, namely, force/force-, force/displacement-, and displacement/displacement-decomposition. Here, we only consider cosimulation methods where the coupling is realized by applied forces/torques, i.e., the case that the coupling between the subsystems is described by constitutive laws. Solver coupling with algebraic constraint equations is not investigated. For the stability analysis, a test model has to be defined. Following the stability definition for numerical time integration schemes (Dahlquist's stability theory), a linear test model is used. The cosimulation test model applied here is a two-mass oscillator, which may be interpreted as two Dahlquist equations coupled by a linear spring/damper system. Discretizing the test model with a cosimulation method, recurrence equations can be derived, which describe the time discrete cosimulation solution. The stability of the recurrence equations system represents the numerical stability of the cosimulation approach and can easily be determined by an eigenvalue analysis.

Stability properties in department of defense contracts: Answering the controversy

Delineating where stability occurs in a contract provides the window of opportunity for procurement officials to positively affect cost and schedule outcomes. While the concept of a Cost Performance Index (CPI) "stability rule" has been routinely cited by Earned Value Management (EVM) authors since the early 1990's, more recent research questions the veracity of this stability rule. This paper resolves the controversy by demonstrating that the definition of stability matters. We find a morphing of the stability definition over time, with three separate definitions permeating the literature. Next, an analysis of Department of Defense contracts for both cost and schedule stability properties finds that the veracity of the stability rule is intricately tied to the definition used.

Stability of tripled fixed point iteration procedures for mixed monotone mappings

Recently, Berinde and Borcut [Berinde, V. and Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4889-4897] introduced the concept of tripled fixed point and by now, there are several researches on this subject, in partially metric spaces and in cone metric spaces. In this paper, we introduce the notion of stability definition of tripled fixed point iteration procedures and establish stability results for mixed monotone mappings which satisfy various contractive conditions. Our results extend and complete some existing results in the literature. An illustrative example is also given.

Development of a Core-Stability Model: A Delphi Approach

Context:Despite widespread acceptance, there is currently no consensus on the definition, components, and the specific techniques most appropriate to measure and quantify core stability.Objective:To develop a comprehensive core-stability model addressing its definition, components, and assessment techniques.Design:Delphi technique.Setting:University laboratory.Participants:15 content experts from United States and Canada, representing a variety of disciplines.Main Outcome Measure:The authors distributed an open-ended questionnaire pertaining to a core-stability definition, components, and assessment techniques specific to each expert. They collected data over 2 rounds of telephone interviews. They concluded data collection once a consensus was achieved that equated with 51% agreement among respondents.Results:The authors developed a working definition of core stability as the ability to achieve and sustain control of the trunk region at rest and during precise movement. Eighty-three percent of the experts considered the definition satisfactory. Therefore, the definition was accepted. Furthermore, the experts agreed that muscles (14/15 = 93.3%) and neuromuscular control (8/12 = 66.7%) were components of core stability. Assessment techniques were identified and inconsistencies were highlighted; however, no consensus was established.Conclusions:A consensus core-stability definition was created and 2 components were identified. However, of the initial definitions provided by the experts, no 2 were identical, which revealed the inconsistencies among experts and the importance of this study. Nonetheless, the goal of obtaining a consensus definition was obtained. Although a consensus for the assessment techniques of core stability could not be reached, it was a beneficial starting point to identify the inconsistencies that were discovered among the content experts.