Event-triggered nonlinear consensus in directed multi-agent systems with combinational state measurements

Event-triggered sampling control is motivated by the applications of embedded microprocessors equipped in the agents with limited computation and storage resources. This paper studied global consensus in multi-agent systems with inherent nonlinear dynamics on general directed networks using decentralised event-triggered strategy. For each agent, the controller updates are event-based and only triggered at its own event times by only utilising the locally current sampling data. A high-performance sampling event that only needs local neighbours’ states at their own discrete time instants is presented. Furthermore, we introduce two kinds of general algebraic connectivity for strongly connected networks and strongly connected components of the directed network containing a spanning tree so as to describe the system's ability for reaching consensus. A detailed theoretical analysis on consensus is performed and two criteria are derived by virtue of algebraic graph theory, matrix theory and Lyapunov control approach. It is shown that the Zeno behaviour of triggering time sequence is excluded during the system's whole working process. A numerical simulation is given to show the effectiveness of the theoretical results.     

Network-based event-triggered filtering for Markovian jump systems

The problem of event-triggered H_∞ filtering for networked Markovian jump system is studied in this paper. A dynamic discrete event-triggered scheme is designed to choose the transmitted data for different Markovian jumping modes. The time-delay modelling method is employed to describe the event-triggered scheme and the network-related behaviour, such as transmission delay, data package dropout and disorder, into a networked Markovian time-delay jump system. Furthermore, a sufficient condition is derived to guarantee that the resulting filtering error system is stochastically stable with a prescribed performance index. A co-design method for the H_∞ filter and the event-triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example.     

Multiple model-based event-triggered adaptive control of a class of discrete-time nonlinear systems

In this study, the problem of event-triggered-based adaptive control (ETAC) for a class of discrete-time nonlinear systems with unknown parameters and nonlinear uncertainties is considered. Both neural network (NN) based and linear identifiers are used to approximate the unknown system dynamics. The feedback output signals are transmitted, and the parameters and the NN weights of the identifiers are tuned in an aperiodic manner at the event sample instants. A switching mechanism is provided to evaluate the approximate performance of each identifier and decide which estimated output is utilised for the event-triggered controller design, during any two events. The linear identifier with an auxiliary output and an improved adaptive law is introduced so that the nonlinear uncertainties are no longer assumed to be Lipschitz. The number of transmission times are significantly reduced by incorporating multiple model schemes into ETAC. The boundedness of both the parameters of identifiers and the system outputs is demonstrated though the Lyapunov approach. Simulation results demonstrate the effectiveness of the proposed method.     

Decentralised event-triggered impulsive synchronisation for semi-Markovian jump delayed neural networks with leakage delay and randomly occurring uncertainties

This study examines the problem of decentralised event-triggered impulsive synchronisation for the semi-Markovian jump neutral type neural networks with leakage delay and randomly occurring uncertainties. An improved globally asymptotic stability criterion is derived to guarantee impulsive synchronisation of the response systems with the drive systems. In order to reduce the network traffic and the resource of computation, we propose a new decentralised event-triggered scheme for the considered delayed NNs. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed. By establishing a suitable Lyapunov–Krasovskii functional (LKF) with triple integral terms and applying Writinger based integral method, auxiliary function based integral inequalities, reciprocal convex approach and improved inequality techniques, a delay dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness of the proposed results.     

Event-triggered MPC Design for Distributed Systems With Network Communications

This paper deals with the communication problem in the distributed system, considering the limited battery power in the wireless network and redundant transmission among nodes. We design an event-triggered model predictive control (ET-MPC) strategy to reduce the unnecessary communication while promising the system performance. On one hand, for a linear discrete time-invariant system, a triggering condition is derived based on the Lyapunov stability. Here, in order to further reduce the communication rate, we enforce a triggering condition only when the Lyapunov function will exceed its value at the last triggered time, but an average decrease is guaranteed. On the other hand, the feasibility is ensured by minimizing and optimizing the terminal constrained set between the maximal control invariant set and the target terminal set. Finally, we provide a simulation to verify the theoretical results. It's shown that the proposed strategy achieves a good trade-off between the closed-loop system performance and communication rate.      

Periodic event-triggering in distributed receding horizon control of nonlinear systems

How to efficiently use limited system resources in distributed receding horizon control (DRHC) is an important issue. This paper studies the DRHC problem for a class of dynamically decoupled nonlinear systems under the framework of event-triggering, to efficiently make use of the computation and communication resources. To that end, a distributed periodic event-triggered strategy is designed and a detailed DRHC algorithm is presented. The conditions for ensuring feasibility of the designed algorithm and stability of the closed-loop system are developed, respectively. We show that the closed-loop system is input-to-state stable if the energy bound of the disturbances, the triggering condition and the cooperation matrices fulfill the proposed conditions.     

Optimum crossing-point estimation of a sampled analog signal with a periodic carrier

The problem of estimating the crossing points of a continuous-time random process, represented by a sequence of uniformly spaced noisy samples, with a periodic analog carrier signal is of crucial importance in the implementation of pulse-width modulation (PWM) and other event-triggered sampling systems. In this paper, we formally approach this problem from a statistical signal processing perspective under a Bayesian framework. We derive the maximum a posteriori (MAP) estimator of the crossing point from a finite sequence of noisy observations, along with a close approximation based on minimum mean squared error (MMSE) considerations. We also study the Bayesian Cramér-Rao bound (CRB) on attainable mean square estimation error. Finally, simulations of a PWM scenario demonstrate that both the MAP and MMSE estimators approach the CRB and outperform several benchmark estimators. The MMSE is a particularly attractive solution as it offers a computationally efficient approximation to the MAP estimator.     

Event-triggered state estimation for Markovian jumping impulsive neural networks with interval time-varying delays

This paper investigates the event-triggered state estimation problem of Markovian jumping impulsive neural networks with interval time-varying delays. The purpose is to design a state estimator to estimate system states through available output measurements. In the neural networks, there are a set of modes, which are determined by Markov chain. A Markovian jumping time-delay impulsive neural networks model is employed to describe the event-triggered scheme and the network- related behaviour, such as transmission delay, data package dropout and disorder. The proposed event-triggered scheme is used to determine whether the sampled state information should be transmitted. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. First, we design a state observer to estimate the neuron states. Second, based on a novel Lyapunov-Krasovskii functional (LKF) with triple-integral terms and using an improved inequality, several sufficient conditions are derived. The derived conditions are formulated in terms of a set of linear matrix inequalities , under which the estimation error system is globally asymptotically stable in the mean square sense. Finally, numerical examples are given to show the effectiveness and superiority of the results.