Region-Searching of Multiple Autonomous Underwater Vehicles: A Distributed Cooperative Path-Maneuvering Control Approach

In this article, a distributed cooperative path-maneuvering control approach is developed for the region-searching of multiple autonomous underwater vehicles under both dynamic uncertainties and ocean currents. Salient contributions are as follows: (1) by virtue of boustrophedon motions and trigonometric functions, the coverage path-planning design is first proposed to generate multiple parameterized paths, which can guarantee that the region-searching is successfully completed by one trial; (2) combining with sliding mode and adaptive technique, distributed maneuvering control laws for surge and yaw motions are employed to drive vehicles to track the assigned paths, thereby contributing to the cooperative maneuvering performance with high accuracy; (3) by the aid of graph theory, the distributed signal observer-based consensus protocols are developed for path parameter synchronization, and successfully apply to maintain the desired formation configuration. The globally asymptotical stability of the closed-loop signals is analyzed via the direct Lyapunov approach, and simulation studies on WL-II are conducted to illustrate the remarkable performance of the proposed path-maneuvering control approach.

Input-to-state Stability in the Meaning of Switching for Delayed Feedback Switched Stochastic Financial System

Financial system is essentially chaotic and unstable if there is not any external inputs. By means of Lyapunov function method, design of switching law, novel fuzzy assumption, $L^p$ estimation technique and Laplace semigroup theory, the author presents the boundedness and LMI-based (globally) asymptotical input-to-state stability criteria of financial systems. Particularly, the globally asymptotical stability in the meaning of switching implies that when the time $t$ is big enough, the dynamic of any subsystem must approach its unique equilibrium point. Besides, the global financial crisis often erupts periodically, which illuminates that the global stability in the classical sense is actually meaningless. So the stability in the meaning of switching proposed in this paper is suitable and appropriate. Numerical examples illuminate the effectiveness of the obtained results.

A Dynamical Behavior of COVID-19 Virus Model with Carrier Effect to Outbreak Epidemic

In this paper, COVID-19 virus model with effect the carrier to outbreak of epidemic is investigated. The outbreak of Covid-19 virus, is described by a mathematical model divided the population into four classes. The first class describes the susceptible unaware to disease, the second class the susceptible with has aware to disease by media coverage, the third class the carrier individuals and the last class is infected individuals. The existence, uniqueness and bounded-ness of the solutions of the model are discussed. All possible equilibrium points are determined. The locally asymptotically stable of the model is studied. Suitable Lyapunov functions are used to investigate the globally asymptotical stability of the model. Finally, numerical simulation is carried out to confirm the analytical results and understand the effect of varying the parameters on spread of disease.

Stability of delay neural networks with uncertainties via delayed intermittent control

In this paper, we investigate the stability of neural networks with both time-varying delays and uncertainties. A novel delayed intermittent control scheme is designed to ensure the globally asymptotical stability of the addressed system. Some new delay dependent sufficient criteria for globally asymptotical stability results are derived in term of linear matrix inequalities (LMIs) by using free-weighting matrix techniques and Lyapunov–Krasovskii functional method. Finally, a numerical simulation is provided to show the effectiveness of the proposed approach.

The Pest Management Model with Impulsive Control

Based on integrated control strategy with spraying pesticides and releasing natural enemies at different fixed moments, we establish a pest management model with impulsive control. Using Floquet theorem of impulsive differential equations and comparison theorem, we obtain the sufficient conditions of globally asymptotical stability of the pest-eradication periodic solution and permanence of the model.

Robust Switched Filtering for Time-Varying Polytopic Uncertain Systems

This paper studies the problem of designing robust switched filters for time-varying polytopic uncertain systems. The synthesis conditions for a set of filters under a min-switching rule are derived to guarantee globally asymptotical stability with optimized robust H∞ performance. Specifically, the conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by linear matrix inequality (LMI) optimization techniques. The proposed approach utilizes a piecewise quadratic Lyapunov function to reduce the conservativeness of robust filtering methods based on single Lyapunov function, thus better H∞ performance can be achieved. Both continuous and discrete-time robust filter designs are considered. To simplify filter implementation, a method to remove redundancy in min-switching filter members is also introduced. The advantages of the proposed robust switching filters are illustrated by several examples.

Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

We formulate a pest management model with periodically releasing infective pests, immature and mature natural enemies, and harvesting pests and crops at two different fixed moments. Sufficient conditions ensuring the locally and globally asymptotical stability of the susceptible pest-eradication period solution are found by means of Floquet theory, small amplitude perturbation techniques, and multicomparison results. Furthermore, the permanence of system is also derived. By numerical analysis, we also show that impulsive releasing and harvesting at two different fixed moments can bring obvious effects on the dynamics of system, which also corroborates our theoretical results.