Abstract This paper is concerned with event-triggered stabilization of a class of nonlinear networked systems. First, a novel event-triggered sampling scheme is proposed based on a monotonically increasing function in the form of the integral of the error norm between the current state and the latest triggered state. It is proven that this scheme ensures the minimum inter-event time to be strictly greater than zero in an explicit expression. Second, a novel Lyapunov functional tailored for the proposed event-triggered scheme is constructed. By applying the looped functional method, a sampling-interval-dependent stabilization criterion is derived. This criterion provides an algorithm to co-design both control gains and event-triggered parameters for a given threshold. Finally, a practical system comprising two identical pendulums is given to demonstrate the effectiveness of the proposed method.

Abstract Event-triggered control (ETC) offers an efficient strategy for significantly reducing communication and computation resources in networked systems by triggering control updates only when necessary. This study provides an overview of recent advances in ETC. First, data-driven (or model-free) ETC, which has gained significant attention in recent years, is reviewed for linear systems with and without unknown disturbances. Second, co-design issues are deeply analyzed for both state feedback and dynamic output feedback control. Third, the separation principle is thoroughly examined in the context of event-triggered observer-based output feedback control. Fourth, some insightful discussions are made on the ideal execution property of event-triggered schemes, as well as the modeling of ETC under packet dropouts. Finally, several challenging issues for future research are outlined.

This article is concerned with the extended dissipativity of discrete-time neural networks (NNs) with time-varying delay. First, the necessary and sufficient condition on matrix-valued polynomial inequalities reported recently is extended to a general case, where the variable of the polynomial does not need to start from zero. Second, a novel Lyapunov functional with a delay-dependent Lyapunov matrix is constructed by taking into consideration more information on nonlinear activation functions. By employing the Lyapunov functional method, a novel delay and its variation-dependent criterion are obtained to investigate the effects of the time-varying delay and its variation rate on several performances, such as$H_\infty $performance, passivity, and$l_{2}-l_\infty $performance, of a delayed discrete-time NN in a unified framework. Finally, a numerical example is given to show that the proposed criterion outperforms some existing ones.

This article deals with collision-risk-based event-triggered optimal formation control problems for mobile multiagent systems. First, several collision-risk-related definitions, such as collision-free margin, moving direction angle, collision risk angle, and collision risk level, are proposed for the moving agents. Then, a collision-risk dependent, time-varying, event-triggered heterogeneous communication network topology is developed, where the agent starts obtaining information of the neighboring agents only when collision risks occur among them. Third, an anti-collision control law, which is composed of a switch function, a control force direction function, and a control strength function, is designed to guarantee the collision avoidance formation of multiagents. Fourth, to ensure the formation quality and save control cost of the multiagent system, an optimal formation control scheme with feedforward compensation is designed. Simulation results illustrate that: 1) by using the collision risk information of mobile agents, the proposed control scheme is effective to realize the collision avoidance optimal formation task and 2) the anti-collision formation controller can be implemented with incomplete information of the agents.

This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov-Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel-Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel-Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

A vibration controller based on wavelet neural network (WNN) is designed for jacket-type offshore platforms with time delay. The offshore platform is regarded as a single-degree-of-freedom (SDOF) system while wave forces are irregular disturbances, and we can rebuild them in the context of Morison equation and wave theory. To reduce the vibration, a WNN vibration controller is designed based on a state feedback optimal control law with memory (SFOCLM). WNN has been widely applied in control problems for its strong capability of adaptive approximation. The tuning rule for updating weights and thresholds of the network is derived to approximate the dynamics of the control system. Data are sampled to train the WNN and the simulation results can prove the feasibility and efficiency in attenuating vibrations.

This paper is concerned with the state estimation for neural networks with two additive time-varying delay components. Three cases of these two time-varying delays are fully considered: 1) both delays are differentiable uniformly bounded with delay-derivative bounded by some constants; 2) one delay is continuous uniformly bounded while the other is differentiable uniformly bounded with delay-derivative bounded by certain constants; and 3) both delays are continuous uniformly bounded. First, an extended reciprocally convex inequality is introduced to bound reciprocally convex combinations appearing in the derivative of some Lyapunov-Krasovskii functional. Second, sufficient conditions are derived based on the extended inequality for three cases of time-varying delays, respectively. Third, a linear-matrix-inequality-based approach with two tuning parameters is proposed to design desired Luenberger estimators such that the error system is globally asymptotically stable. This approach is then applied to state estimation on neural networks with a single interval time-varying delay. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

This paper provides an overview and makes a deep investigation on sampled-data-based event-triggered control and filtering for networked systems. Compared with some existing event-triggered and self-triggered schemes, a sampled-data-based event-triggered scheme can ensure a positive minimum inter-event time and make it possible to jointly design suitable feedback controllers and event-triggered threshold parameters. Thus, more attention has been paid to the sampled-data-based event-triggered scheme. A deep investigation is first made on the sampled-data-based event-triggered scheme. Then, recent results on sampled-data-based event-triggered state feedback control, dynamic output feedback control, H∞filtering for networked systems are surveyed and analyzed. An overview on sampled-data-based event-triggered consensus for distributed multiagent systems is given. Finally, some challenging issues are addressed to direct the future research.

This paper is concerned with networked output feedback H∞control of an offshore structure under earthquakes. With a networked model of the offshore structure, a networked output feedback H∞control strategy is proposed to suppress seismic vibration of the structure. Then, some delay-dependent stability criteria for the offshore structure system are derived. Simulation results show that compared with traditional network-free controllers, the networked output feedback H∞controller can mitigate vibration of the offshore structure and control cost to a smaller level.

This paper provides a brief overview of delayed feedback control schemes for offshore structures. Two simplified models of offshore steel jacket structures are listed first. Then based on the dynamic models of offshore structures, several active control strategies including delayed H∞control and delayed integral sliding mode control by using pure delayed signals and using current as well as delayed signals of the systems are outlined, respectively. Finally, some challenging problems and potential research directions about delayed feedback control for offshore structures are presented.

This paper is concerned with the problem of the robust sampled-data H∞ control for an offshore steel jacket platform subject to the self-excited wave force and the external disturbance. First, by using the input delay method, the corresponding closed-loop system with the sampling measurements is transformed into a continuous-time system. Then, based on a Lyapunov functional, the H∞ performance is established and the stability criteria for the closed-loop system is derived. Finally, the effectiveness of the proposed robust sampled-data H∞ controller is demonstrated by a simulation example. The simulation results show that the designed controller is effective to control the offshore platform, Moreover, to obtain almost the same control performance, the required control force under the robust sampled-data H∞ controller is smaller than the one under the robust H∞ controller.

This paper is concerned with network-based H∞control for an offshore steel jacket platform subject to nonlinear wave-induced force and external disturbance. A network-based dynamic model of the offshore platform with an active tuned mass damper mechanism is presented, and a network-based H∞control scheme is presented to attenuate the vibration of the offshore platform. The effects of the network-induced delays on the H∞control for the offshore platform is investigated. Simulation results show that the proposed network-based H∞control scheme can improve the control performance of the offshore platform significantly. In addition, the control force and the oscillation amplitudes of the offshore platform under the network-based H∞controller with proper network-induced delays are smaller than the ones under the H∞controller without network settings, which means that the proper network-induced delays are of the positive effects on the H∞control of the offshore platform.

This paper is concerned with delay-dependent robust H∞control for an offshore steel jacket platform subject to wave force. By taking into account the variations of the structural natural frequency and damping ratio, and time-varying control delay, an uncertain time-delay dynamic modal of the offshore platform is established first. Then a delay-dependent robust H∞control scheme is proposed to attenuate the wave-induced vibration of the platform. A delay-dependent robust H∞controller is obtained in terms of the solvability of a nonlinear minimization problem. Simulation results show that though there exist time-varying control delay and parameter uncertainties in the system, the designed controller can effectively attenuate the vibration of the offshore platform and keep the stability of the system.

This paper is concerned with network-based control for an offshore steel jacket platform subject to nonlinear wave-induced force. A network-based dynamic model of the offshore platform is presented and a network-based state feedback control scheme is developed to reduce the internal oscillations of the offshore platform. Then the effect of a network-induced delay on the control performance of the offshore platform is investigated. It is found through simulation results that (i) the network-based state feedback controller is of a smaller gain in the sense of Euclidean norm than the state feedback controller without network setting, which means the network-based state feedback controller requires less control force; and (ii) the network-induced delay is of the positive effect on state feedback control of the offshore platform.

This paper is concerned with non-fragile H∞control for offshore steel jacket platforms subject to self-excited nonlinear wave force and external disturbances. A delayed non-fragile H∞controller is designed to attenuate the oscillation amplitudes of the offshore platform. The positive effects of the time-delays on non-fragile H∞control for the offshore platform are investigated. It is shown through simulation results that (i) the proposed non-fragile H∞controller is effective to reduce the vibration of the offshore platform; (ii) the control force required by the delayed non-fragile H∞controller is smaller than the one by the delay-free non-fragile H∞controller; and (iii) the allowable maximum time-delay under the delayed non-fragile H∞controller is much larger than the one under the delayed dynamic output feedback controller.

Based on the quadratic cost functional index, the optimal control problem of linear discrete-time control systems affected by external persistent disturbances is developed. The main result concerns the existence and design of a realizable, robust feedforward and feedback optimal control law. It is shown that the optimal control law is realizable easily and more robust with respect to additive disturbances than that one of the classical feedback optimal control through simulation.