Journal of Systems Science and Complexity

This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances. In case there is no perturbation, the exponential convergence of the observer was confirmed. When external disturbances appear in the system, a separation principle is established, and the authors show that the closed loop system is exponentially practical stable. By choosing a suitable Lyapunov-Krasovskii functional, the authors derive new sufficient conditions to guarantee the exponential stability of the systems. Finally, a physical model is performed to prove the efficiency and applicability of the suggested approach.

Model average receives much attention in recent years. This paper considers the semiparametric model averaging for high-dimensional longitudinal data. To minimize the prediction error, the authors estimate the model weights using a leave-subject-out cross-validation procedure. Asymptotic optimality of the proposed method is proved in the sense that leave-subject-out cross-validation achieves the lowest possible prediction loss asymptotically. Simulation studies show that the performance of the proposed model average method is much better than that of some commonly used model selection and averaging methods.

This paper is concerned with the multi-agent systems with both packet dropout and input delay. A novel receding horizon control (RHC) based consensus protocol is proposed by solving a distributed RHC based optimization problem. The novelty of the optimization problem lines in the involvement of the neighbours’ predictor information in the cost functions. Based on the derived RHC based consensus protocol, the necessary and sufficient condition for the mean-square consensus is obtained. In addition, the authors give a specific sufficient condition to guarantee the mean-square consensus.

Motivated by the idea of Shen, et al.’s work, which proposed a hybrid procedure for real root isolation of polynomial equations based on homotopy continuation methods and interval analysis, this paper presents a hybrid procedure to compute sample points on each connected component of a real algebraic set by combining a special homotopy method and interval analysis with a better estimate on initial intervals. For a real algebraic set given by a polynomial system, the new method first constructs a square polynomial system which represents the sample points, and then solve this system by a special homotopy continuation method introduced recently by Wang, et al. (2017). For each root returned by the homotopy continuation method, which is a complex approximation of some (complex/real) root of the polynomial system, interval analysis is used to verify whether it is an approximation of a real root and finally get real points on the given real algebraic set. A new estimate on initial intervals is presented which helps compute smaller initial intervals before performing interval iteration and thus saves computation. Experiments show that the new method works pretty well on tested examples.

This paper aims to contribute to the literature on the explanatory power of behavior models with heterogeneous agents. The authors present a new nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. An exogenous noise is introduced to the model with the assumption of IID normal innovations of the fundamental value in order to investigate how noisy dynamics interacts with deterministic process. The market is composed of two typical trader types: the rational fundamentalists and the boundedly rational traders governed by greed and fear. The interaction between noise and deterministic element determines the evolution process of the system as key parameters are changed. The authors find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S&P500 index, such as volatility clustering, fat tails (leptokurtosis), autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. The authors also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach.

This paper studies a maintenance model for an one-unit degenerative system with multiple failure states based on the proportional hazards and proportional reversed hazards models. The authors investigate how the variation of system configuration parameters have an impact on both operating and repair times and hence the system performance. Furthermore, the authors also derive the explicit expression for the long-run average cost per unit time. An algorithm to locate the optimal number of repairs in a renewal cycle is discussed as well.