Opinion consensus incorporating higher-order interactions in individual-collective networks

In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.

THE PROBABILITY STABILITY OF VISCOELASTIC PLATES

The almost sure stability of homogeneous viscoelastic platessubjected to a random wide-band stationary in-plane load isinvestigated. The viscoelastic behavior of the plate is described interms of the Bo- ltzmann superposition principle, the relaxationkernels of which are represented by the sums of exponents. On theassumption that the in-plane load is random wide-band stationaryprocess, sufficient conditions for al- Most sure stability ofviscoelastic plates are obtained by the applications of Lyapunov'sdirect method.

A Lyapunov characterization of robust policy optimization

In this paper,we study the robustness property of policy optimization(particularly Gauss-Newton gradient descent algorithm which is equivalent to the policy iteration in reinforcement learning)subject to noise at each iteration.By invoking the concept of input-to-state stability and utilizing Lyapunov's direct method,it is shown that,if the noise is sufficiently small,the policy iteration algorithm converges to a small neighborhood of the optimal solution even in the presence of noise at each iteration.Explicit expressions of the upperbound on the noise and the size of the neighborhood to which the policies ultimately converge are provided.Based on Willems'fundamental lemma,a learning-based policy iteration algorithm is proposed.The persistent excitation condition can be readily guaranteed by checking the rank of the Hankel matrix related to an exploration signal.The robustness of the learning-based policy iteration to measurement noise and unknown system disturbances is theoretically demonstrated by the input-to-state stability of the policy iteration.Several numerical simulations are conducted to demonstrate the efficacy of the proposed method.

A Sliding Mode Controller Based on Robust Model Reference Adaptive Proportional-integral Control for Stand-alone Three-phase Inverter

This paper proposes a sliding mode controller based on robust model reference adaptive proportional-integral(RMRA-PI)control for a stand-alone voltage source inverter(SA-VSI).The proposed controller has two control loops where the coefficients of PI controller are regulated by the adaptive sliding law.This method is used to regulate the output voltage of the inverter under different load conditions and uncertainty,and adapts the output to the reference model to reduce the total harmonic distortion(THD).In this paper,the stability of the proposed controller is proven by using Lyapunov's theory and Barbalet’s lemma.The proposed controller performs well in voltage regulation such as low THD under sudden load change and uncertainty.Also,the results of the proposed controller are compared with PI controller to show the effectiveness of the presented control system.