A globally convergent BFGS method for pseudo-monotone variational inequality problems

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.     

Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control

The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved.     

Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration

In this paper numerical approximation of history-dependent hemivariational inequalities with constraint is considered, and corresponding Céa’s type inequality is derived for error estimate. For a viscoelastic contact problem with normal penetration, an optimal order error estimate is obtained for the linear element method. A numerical experiment for the contact problem is reported which provides numerical evidence of the convergence order predicted by the theoretical analysis.     

匹配机械弹性车轮的电子稳定控制器参数分析

为了提高匹配机械弹性车轮(MEW)的某越野车操纵稳定性，考虑MEW与传统子午线轮胎侧偏特性存在的不确定性摄动，基于Lyapunov稳定性理论为电子稳定控制(ESC)程序设计了鲁棒反馈控制器；引入轮胎侧偏刚度不确定性的范数有界模型，运用Schur补引理和线性矩阵不等式(LMI)求解反馈矩阵。设定不同的车速和路面附着系数，通过搭建CarSim/Simulink联合仿真平台对控制器展开鱼钩试验，仿真结果表明，匹配MEW的ESC控制器能够保证车辆行驶的稳定性，横摆角速度与质心侧偏角跟踪误差分别稳定在0.03~0.3 rad/s与0.06~0.1 rad之内，并且设计的控制算法对MEW在05倍普通充气车轮侧偏刚度变化范围内具有很好的鲁棒性，从而为匹配MEW的整车主动安全控制提供了理论参考。     

Increasing inequalities in what we do online: A longitudinal cross sectional analysis of Internet activities among the Dutch population (2010 to 2013) over gender,age, education,and income

We investigate types of Internet activities among a representative sample of the Dutch population from 2010 to 2013. We examined usage patterns of seven types of Internet activities (i.e., information, news, personal development, commercial transaction, social interaction, leisure, and gaming) and related these patterns with gender, age, education, and income. Activities related to news, personal development, commercial transaction, and social interaction increased in popularity. For most capital enhancing activities, men, younger people, higher educated people, and people with higher than average incomes were prominent. These observations, however, are subject to change. The Internet seems to provide increasingly more capital-enhancing opportunities for those with higher education and income, which would accordingly reinforce their already strong positions in society.     

Reduced-order multiple observer for Takagi–Sugeno systems with unknown inputs

The paper discusses a niche area problem — the design of reduced-order multiple observers which can achieve the finite-time state reconstruction for Takagi–Sugeno multiple models with unknown inputs. The new reduced-order multiple observer obtained in this paper is only the second ever designed, the author of this paper continuing his work started one year ago with the introduction of the reduced-order multiple observer concept. The obtaining of the new reduced-order multiple observer is achieved by combining two classical reduced-order observers for linear time-invariant multivariable systems with unknown inputs and a full-order multiple observer for Takagi–Sugeno systems. The main innovative idea behind the design of the reduced-order multiple observer for Takagi–Sugeno systems described by the multiple models is the split of the multiple model into two subsystems: an unknown-input-free subsystem and an unknown-input-depending subsystem. The unknown-input-free subsystem is brought to the form of a standard multiple model and, in this situation, any algorithm to design full-order multiple observers can be used in the design of reduced-order multiple observers. The steps of the design procedure have been summarized and software implemented; then, the validation of the suggested algorithm has been done for two concrete cases associated to the motion of an aircraft during its landing     

Robust predictive extended state observer for a class of nonlinear systems with time-varying input delay

ABSTRACT

This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.     

Leader-following consensus of fractional-order multi-agent systems via adaptive control

This article focuses on the consensus problem of leader-following fractional-order multi-agent systems (MASs) with general linear and Lipschitz nonlinear dynamics. First, the distributed adaptive protocols for linear and nonlinear fractional-order MASs are constructed, respectively. We allow the control coupling gains to be time varying for each agent. Moreover, the adaptive modification schemes for the control gain are designed, which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence. Second, based on fractional-order Lyapunov stability theorem and Barbalat's lemma, two novel sufficient conditions in terms of linear matrix inequalities are provided to ensure that the leader-following consensus can be obtained in the case for any undirected connected communication graph. Furthermore, we show that the proposed algorithm also works for consensus of agents with intrinsic Lipschitz nonlinear dynamics. As a result, the proposed framework requires no global information and thus can be implemented in a fully distributed manner. Finally, the numerical simulations are given to demonstrate the effectiveness of obtained the theoretical results.     

Robust Control of Permanent Magnet Synchronous Motors

In this paper, permanent magnet synchronous motors (PMSMs) are investigated. According to the feature of PMSMs, a novel state equation of PMSMs is obtained by choosing suitable state variables. Based on the state equation, robust controllers are designed via interval matrix and PI control idea. In terms of bilinear matrix inequations, sufficient conditions for the existence of the robust controller are derived. In order to reduce the conservation and the dependence on parameter, the control inputs of PMSMs are divided into two parts, a feedforward control input and a feedback control input, and relevant sufficient conditions for the existence of the controller are obtained. Because of the suitable choice of state variables, the proposed control strategies can cope with the load uncertainty and have robustness for disturbance. Finally, simulations are carried out via Matlab/Simulink soft to verify the effectiveness of the proposed control strategies. The performance of the proposed control strategies are demonstrated by the simulation results.      

Robust user equilibrium model based on cumulative prospect theory under distribution-free travel time

The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.