In this paper, we study the consensus problem for a class of linear multiagent systems, where the communication networks are directed First, a dynamic event-triggering mechanism is introduced, including some existing static event-triggering mechanisms as its special cases Second, based on the dynamic event-triggering mechanism, a distributed control protocol is developed, which ensures that all agents can reach consensus with an exponential convergence rate Third, it is shown that, with the dynamic event-triggering mechanism, the minimum interevent time between any two consecutive triggering instants can be prolonged and no agent exhibits Zeno behavior Finally, an algorithm is provided to avoid continuous communication when the dynamic event-triggering mechanism is implemented The effectiveness of the results is confirmed through a numerical example

A Distributed Dynamic Event-Triggered Control Approach to Consensus of Linear Multiagent Systems With Directed Networks

Non-negative latent factor (NLF) models can efficiently acquire useful knowledge from high-dimensional and sparse (HiDS) matrices filled with non-negative data. Single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) is an efficient algorithm for building an NLF model on an HiDS matrix, yet it suffers slow convergence. A momentum method is frequently adopted to accelerate a learning algorithm, but it is incompatible with those implicitly adopting gradients like SLF-NMU. To build a fast NLF (FNLF) model, we propose a generalized momentum method compatible with SLF-NMU. With it, we further propose a single latent factor-dependent non-negative, multiplicative and momentum-incorporated update algorithm, thereby achieving an FNLF model. Empirical studies on six HiDS matrices from industrial application indicate that an FNLF model outperforms an NLF model in terms of both convergence rate and prediction accuracy for missing data. Hence, compared with an NLF model, an FNLF model is more practical in industrial applications.

/pdf/a-fast-non-negative-latent-factor-model-based-on-generalized-1gpdeufjz2.pdf

A Fast Non-Negative Latent Factor Model Based on Generalized Momentum Method

This paper deals with the co-design problem of event-triggered communication scheduling and platooning control over vehicular ad-hoc networks (VANETs) subject to finite communication resource. First, a unified model is presented to describe the coordinated platoon behavior of leader-follower vehicles in the simultaneous presence of unknown external disturbances and an unknown leader control input. Under such a platoon model, the central aim is to achieve robust platoon formation tracking with desired inter-vehicle spacing and same velocities and accelerations guided by the leader, while attaining improved communication efficiency. Toward this aim, a novel bandwidth-aware dynamic event-triggered scheduling mechanism is developed. One salient feature of the scheduling mechanism is that the threshold parameter in the triggering law is dynamically adjusted over time based on both vehicular state variations and bandwidth status. Then, a sufficient condition for platoon control system stability and performance analysis as well as a co-design criterion of the admissible event-triggered platooning control law and the desired scheduling mechanism are derived. Finally, simulation results are provided to substantiate the effectiveness and merits of the proposed co-design approach for guaranteeing a trade-off between robust platooning control performance and communication efficiency.

Dynamic Event-Triggered Scheduling and Platooning Control Co-Design for Automated Vehicles Over Vehicular Ad-Hoc Networks

In this paper we consider the class of discrete-time switched systems switching between p autonomous positive subsystems. First, sufficient conditions for testing stability, based on the existence of special classes of common Lyapunov functions, are investigated, and these conditions are mutually related, thus proving that if a linear copositive common Lyapunov function can be found, then a quadratic positive definite common function can be found, too, and this latter, in turn, ensures the existence of a quadratic copositive common function. Secondly, stabilizability is introduced and characterized. It is shown that if these systems are stabilizable, they can be stabilized by means of a periodic switching sequence, which asymptotically drives to zero every positive initial state. Conditions for the existence of state-dependent stabilizing switching laws, based on the values of a copositive (linear/quadratic) Lyapunov function, are investigated and mutually related, too. Finally, some properties of the patterns of the stabilizing switching sequences are investigated, and the relationship between a sufficient condition for stabilizability (the existence of a Schur convex combination of the subsystem matrices) and an equivalent condition for stabilizability (the existence of a Schur matrix product of the subsystem matrices) is explored.

Stability and Stabilizability Criteria for Discrete-Time Positive Switched Systems

Fault detection of networked dynamical systems (NDSs) has attracted ever-increasing attention since it can maintain high-quality products as well as operational safety. Considering the utilisation ...

https://www.tandfonline.com/doi/pdf/10.1080/00207721.2021.1998722

Fault detection of networked dynamical systems: a survey of trends and techniques

This paper is concerned with the synchronization control problem for a class of discrete time-delay complex dynamical networks under a dynamic event-triggered mechanism. For the efficiency of energy utilization, we make the first attempt to introduce a dynamic event-triggering strategy into the design of synchronization controllers for complex dynamical networks. A new discrete-time version of the dynamic event-triggering mechanism is proposed in terms of the absolute errors between control input updates. By constructing an appropriate Lyapunov functional, the dynamics of each network node combined with the introduced event-triggering mechanism are first analyzed, and a sufficient condition is then provided under which the synchronization error dynamics is exponentially ultimately bounded. Subsequently, a set of the desired synchronization controllers is designed by solving a matrix inequality. Finally, a simulation example is provided to verify the effectiveness of the proposed dynamic event-triggered synchronization control scheme.

Synchronization Control for A Class of Discrete Time-Delay Complex Dynamical Networks: A Dynamic Event-Triggered Approach

In this paper, we consider a linear wave equation on an interval with a van der Pol nonlinear boundary condition at one end and an energy-pumping condition at the other end. We study the dynamical behavior of the Riemann invariants (u,v) of the wave equation in terms of the growth rates of the total variations of the snapshots on the spatial interval. Our main contributions here are the detection of rapid fluctuations of the snapshots of u and v in the long run. The results here sharpen those in the earlier works of [Chen et al., 2001] and [Huang, 2003].

Rapid fluctuations of snapshots of one-dimensional linear wave equation with a van der pol nonlinear boundary condition

The set of stable switching sequences for discrete-time linear switched systems☆

The packing measure of the Cartesian product of the middle third Cantor set with itself

. A Peano compactum is a compact metric space with locally connected components such that at most ﬁnitely many of them are of diameter greater than any ﬁxed number C > 0. Given a compactum K in the extended complex plane ˆ C . It is known that there is a ﬁnest upper semi-continuous decomposition of K into subcontinua such that the resulted quotient space is a Peano compactum. We call this decomposition the core decomposition of K with Peano quotient and its elements atoms of K . For any atom of K and any ﬁnite-to-one open map f : ˆ C → ˆ C , we show that every component of f − 1 ( d ) is also an atom of f − 1 ( K ). Since all rational functions are ﬁnite-to-one open maps, our result extends earlier ones that are restricted to more limited cases, requiring that f be a polynomial with f − 1 ( K ) = K . We also determine the atoms for typical planar continua. In particular, we show that every quadratic Julia set J that contains a Cremer ﬁxed point has a unique atom, the whole Julia set J .

pdf/a-model-for-planar-compacta-and-rational-julia-sets-1alps8eo.pdf

A model for planar compacta and rational Julia sets

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