We study the Abreu's equation in n-dimensional polytopes and derive interior estimates of solutions under the assumption of the uniform K-stability.
This paper investigates the effects of coupling delays on synchronization in Lur'e complex dynamical networks. Every identical node in the network can be represented as a Lur'e system. Based on Lyapunov–Krasovskii functionals and Lur'e–Postnikov Lyapunov functionals, some delay-dependant synchronization criteria are derived by employing a delay decomposition approach. A Lur'e complex dynamical network with Chua's circuit nodes and one numerical example are given to illustrate the effectiveness of the synchronization criteria.
The paper is concerned with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus control problem for discrete-time stochastic multi-agent systems with both additive and multiplicative noises. A novel control protocol, namely, PD-type (proportional-derivative-type) control protocol, is proposed to improve the consensus dynamics. By resorting to the well-known Lyapunov stability theory and the matrix inequality techniques, some sufficient conditions are developed to guarantee the considered H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus. Furthermore, the analytical formula of the controller gains is established with help from the singular value decomposition approach. Finally, the effectiveness of the proposed consensus control scheme is demonstrated through a numerical simulation example.
No abstract is provided for this article.
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.
This paper is concerned with the network-based modeling, and observer-based fault detection filter (FDF) and controller coordinated design for an unmanned surface vehicle (USV) in network environments. Network-based models for the USV subject to actuator faults and wave-induced disturbances are established for the first time by introducing an observer-based FDF, and considering network-induced characteristics such as delays and packet dropouts in the sampler-to-control station communication network channel and the control station-to-actuator communication network channel. Based on these models, network-based FDF and controller coordinated design criteria are derived to asymptotically stabilize the residual system. The designed network-based FDF and controller can guarantee the sensitivity of the residual signal to faults and the robustness of the USV to external disturbances. Fault detection performance analysis verifies the effectiveness of the proposed network-based FDF and controller coordinated design scheme for the USV in network environments.
In this paper, we study the existence of smooth local solutions to Weingarten equations and $\sigma_k$-equations. We will prove that, for $2 \leq k \leq n$, the Weingarten equations and the $\sigma_k$-equations always have smooth local solutions regardless of the sign of the functions in the right-hand side of the equations. We will demonstrate that the associate linearized equations are uniformly elliptic if we choose the initial approximate solutions appropriately.
This paper investigates network-based fuzzy static output feedback tracking control for Van der Pol's oscillators using positive effects of network-induced delays. Taking network-induced delays into account, the network-based nonlinear control system is modeled as an asynchronous T-S fuzzy system with an interval time-varying delay. A discontinuous complete Lyapunov-Krasovskii functional and a new relaxation method involving the asynchronous constraints on membership functions are proposed to derive some delay-dependent criteria on H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking performance analysis and controller design of the asynchronous fuzzy system. The effectiveness of the proposed method is shown by a numerical example.
Fixed-time cooperative control is currently a hot research topic in multiagent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multiagent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multiagent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then, recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.
This paper deals with the problem of odor source localization using a multi-robot system. Taking limited communication networks among the multi-robot system into account, a new cooperative search algorithm, namely, a probability particle swarm optimizer with information-sharing mechanism, is proposed and independently executed by each robot, by which the team of robots can be efficiently coordinated to locate a stationary odor source. In order to develop the proposed algorithm, an information-sharing matrix, which is used to store information by learning from the position information of robots, is designed. Based on the matrix, the probable position of the odor source as the new position of the robot is produced by following three simple steps. Finally, the effectiveness of the proposed algorithm is illustrated in the problem of odor source localization.
This paper is concerned with the event-triggered H ∞ control for a nonlinear networked control system. A new event-triggered transmission scheme is first proposed to reduce the network bandwidth utilization. Under this scheme, the nonlinear networked control system is formulated as a Takagi–Sugeno fuzzy threshold-error-dependent system with asynchronous normalized membership functions. Then, by using the deviation bounds of asynchronous normalized membership functions, some sufficient conditions on the existence of the parameters of the event-triggered transmission scheme and the fuzzy controller are derived such that the Takagi–Sugeno fuzzy threshold-error-dependent system with asynchronous normalized membership functions is asymptotically stable with a prescribed H ∞ attenuation level. It is shown that the proposed design method can reduce the conservativeness of some existing results. Finally, two examples are given to demonstrate the effectiveness of the proposed design method and the event-triggered transmission scheme.
This paper investigates synchronization of dynamical networks with both system delay and transmission delay by applying pinning impulsive control. Based on the comparison theorem and the theory of impulsive functional differential equations, some novel criteria are obtained, from which the proportion of pinned nodes is able to be determined. A numerical example is given to verify the effectiveness of the theoretical results.
