Dual switching system is a special hybrid system that contains both deterministic and stochastic switching subsystems. Due to its complex switching mechanism, few studies have been conducted for dual switching systems, especially for systems with uncertainty. Usually, the stochastic subsystems are described as Markov jump systems. Based upon the upstanding identity of RBF neural network on approaching nonlinear data, the tracking models for uncertain subsystems are constructed and the neural network adaptive controller is designed. The global asymptotic stability almost surely (GAS a.s.) and almost surely exponential stability (ES a.s.) of dual switching nonlinear error systems are investigated by using the energy attenuation theory and Lyapunov function method. An uncertain dual switching system with two subsystems, each with two modes, is studied. The uncertain functions of the subsystems are approximated well, and the approximation error is controlled to be below 0.05. Under the control of the designed adaptive controller and switching rules, the error system can obtain a good convergence rate. The tracking error is quite small compared with the original uncertain dual switching system.
We aim to refine the estimation of the finite stopping time when the disagreement in an opinion group is eliminated by a simple but novel noise intervened strategy. It has been proved that, by using this noise intervened control strategy, the divisive opinions would get synchronized in finite time. Moreover, the finite stopping time when resolving the disagreement has been clarified. The estimation of the finite stopping time will effectively reveal which factors and how they determine the consequence of intervention. However, the upper bound for the estimation of the integrable stopping time when noise is oriented has been quite conservative. In this paper, we investigate the finite stopping time of eliminating the disagreement by completely oriented noise and a much more precise formula for the estimation of the finite stopping time is obtained finally via direct calculation.
In this paper, we study the noise-induced truth seeking for heterogeneous Hegselmann-Krause (HK) model in opinion dynamics. It has been proved that small noise could induce the group to achieve truth in homogeneous HK model; however, for the more practical heterogeneous HK model, the theoretical conclusion is absent. Here, we prove that small noise could also induce the group to achieve truth in heterogenous HK model, and, moreover, we first theoretically prove that large noise could drive some agents to deviate from the truth. These theoretical findings evidently reveal how the free information flow spreading in the media determines the social truth seeking.
In this paper, we address the almost sure stability problem of Caputo fractional-order Markovian switching nonlinear systems. Firstly, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of Caputo fractional-order Markovian switching nonlinear systems (CFMNSs) with the constant lower bound initial time, some sufficient conditions are given by the stochastic Multi-Lyapunov function and probability analysis method. Then, for CFMNSs with the variable lower bound initial time, a resetting CFMNSs model is constructed to update synchronously the lower bound initial time and the corresponding initial state value of the above-mentioned system with the change of switching. After that, for CFMNSs with the variable lower bound initial time under the resetting means, the sufficient conditions of GAS a.s. and ES a.s. are given using the probability analysis method and stochastic Multi-Lyapunov function, respectively. Finally, numerical examples show that our results are effective.
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