In the process of rumor spreading, controlling and killing rumor problem is of great importance on social networks. In this paper, we present a new SEIR (susceptible-exposed-infected-removed) rumor spreading model with hesitating mechanism. By using mean-field theory, the equilibrium of the model and the basic reproduction number \(R_{0}\) are obtained. The global stability of the rumor-free equilibrium and the permanence are proved in detail, and the global attractivity of the rumor-prevailing equilibrium is proved by using a monotone iterative technique. Furthermore, the modified model with feedback mechanism on social networks is introduced. The feedback mechanism cannot change the basic reproductive number but it can reduce the continuous level and the spread of rumor. Numerical simulations confirm the analytical results.

This article studies the formation tracking control (FTC) of nonlinear second-order leader–following multiagent systems (LFMASs) with time-varying delays and periodic sampling. The FTC protocols based on position and velocity information of neighbor agents and measurable communication noise in fixed and Markovian switching directed topology are proposed. Some sufficient conditions are obtained to reach formation tracking by using the algebraic graph theory and generalized Halanay inequality. Meanwhile, the upper bound of formation-able time-varying delays $\bar{\tau }$ is obtained. Results show that the LFMASs can achieve formation tracking in mean-square exponential stability as well as almost sure exponential stability under the proposed control algorithms. Finally, the availability of the theoretical results is verified by numerical simulation.

Gait plays a decisive role in the performance of hexapod robot walking; this paper focuses on adaptive gait generation with reinforcement learning for a hexapod robot. Moreover, the hexapod robot has a high-dimensional action space and therefore it is a great challenge to use reinforcement learning to directly train the robot’s joint angles. As a result, a hierarchical and modular framework and learning details are proposed in this paper, using only seven-dimensional vectors to denote the agent actions. In addition, we conduct experiments and deploy the proposed framework using a real hexapod robot. The experimental results show that superior reinforcement learning algorithms can converge in our framework, such as SAC, PPO, DDPG and TD3. Specifically, the gait policy trained in our framework can generate new adaptive hexapod gait on flat terrain, which is stable and has lower transportation cost than rhythmic gaits.

This paper mainly studies the transition gait planning by updating the parameters of snack robot motion control function through ROS nodes, including a straight running gait into a turning gait. In the practical scenario, when changing the control parameters, the joint angle of the snake robot will increase or decrease sharply, and the angular velocity and angular acceleration of the driving joints will also change, which results in oscillation and sideslip of the body. In the turning scene, the visual tracking will loss if the head joint of the snake robot causes the lateral movement and oscillation. To solve those problems, firstly, the dynamic model of the snake robot’s gait of serpentine movement is established. Then, we propose a method based on polynomial interpolation compensation to solve the body oscillation and sideslip caused by nodes updating. To further improve the efficiency of snake robot’s gait switching, an optimal dichotomy interpolation time search is proposed to realize the snake robot’s adaptive transition gait. Finally, some simulation experiments are verified the effectiveness of the proposed method.

In article, we study the problem of aperiodically intermittent control (APIC) for neutral stochastic delay systems (NSDSs) based on discrete observations. To overcome the difficulty caused by intermittent control, an auxiliary system is introduced. By using the Lyapunov function method, an upper bound of observation period $\delta ^{*}$ is obtained. If observation period $\delta < \delta ^{*}$ , then the auxiliary system is $p$ th $(p\geq 2)$ -moment exponentially stable. In addition to the fixed observation period $\delta < \delta ^{*}$ , this article gives a method to design an aperiodically intermittent controller and obtains a lower bound of duty cycle for all fixed $0 < \underline {T}\leq \overline {T}$ with $\underline {T}$ and $\overline {T}$ being lower bound and upper bound of control frames. That is, we proved the NSDSs with the intermittent discrete observation controller is $p$ th $(p\geq 2)$ -moment exponentially stable if the auxiliary system is $p$ th $(p\geq 2)$ -moment exponentially stable. We call this method the auxiliary system method (ASM). In fact, different from mainstream techniques, the ASM used in this article can handle the case of $0 < \underline {T}\leq \overline {T} < \delta $ even if $\delta $ is small enough. Besides, this article reveals one interesting phenomenon: classic methods may lead to error accumulation, which cannot be avoided in APIC or periodically intermittent control (PIC) for NSDSs. Finally, one numerical example, one application, and one comparison are given to show the usefulness and correctness of the proposed results.