Inter-execution Time Research Articles

Dynamic event-triggered consensus for stochastic delay multi-agent systems under directed topology

This paper addresses the mean-square exponential consensus (MSEC) challenge in stochastic delay multi-agent systems (MASs) under directed topology. The main contributions include avoiding infinitely fast sampling and conducting a random stability analysis. First, a dynamic event-triggered mechanism (DETM) with a fixed positive lower bound for the inter-execution time is designed to prohibit Zeno behavior. The proposed control strategy does not involve the expectations of system signals. Then, sampling errors are estimated using Itô isometry, which ensures that the fixed control at each work interval is maintained with adequate feedback capacity to mitigate the effects of these errors. Furthermore, with the help of a Halanay inequality in integral form and Lyapunov theorem framework, some conditions are proposed to guarantee the consensus of stochastic delay MASs under directed topology. Finally, an example is presented to prove the effectiveness of the DETM method.

ADP-Based Event-Triggered Constrained Optimal Control on Spatiotemporal Process: Application to Temperature Field in Roller Kiln.

The precise control of the spatiotemporal process in a roller kiln is crucial in the production of Ni-Co-Mn layered cathode material of lithium-ion batteries. Since the product is extremely sensitive to temperature distribution, temperature field control is of great significance. In this article, an event-triggered optimal control (ETOC) method with input constraints for the temperature field is proposed, which takes up an important position in reducing the communication and computation costs. A nonquadratic cost function is adopted to describe the system performance with input constraints. First, we present the problem description of the temperature field event-triggered control, where this field is described by a partial differential equation (PDE). Then, the event-triggered condition is designed according to the information of system states and control inputs. On this basis, a framework of the event-triggered adaptive dynamic programming (ETADP) method that is based on the model reduction technology is proposed for the PDE system. A critic network is used to approach the optimal performance index by a neural network (NN) together with that an actor network is used to optimize the control strategy. Furthermore, an upper bound of the performance index and a lower bound of interexecution times, as well as the stabilities of the impulsive dynamic system and the closed-loop PDE system, are also proved. Simulation verification demonstrates the effectiveness of the proposed method.

Global regulation of almost feedforward nonlinear systems by an adaptive event‐triggered controller with multi‐triggering conditions

AbstractWe consider a global regulation problem for almost feedforward nonlinear systems with uncertain time‐varying parameters using an adaptive event‐triggered controller. The systems we consider are called “almost” feedforward systems because, in addition to the feedforward nonlinearity with the unknown linear growth rate, there is a non‐zero input‐matching term. Notably, this input‐matching term is a non‐feedforward term and it cannot be directly canceled due to the presence of input uncertainty and the use of event‐triggered control. To solve our considered problem, we propose an adaptive event‐triggered controller with multi‐triggering conditions and dynamic gain. We show that the closed‐loop system is globally regulated and the times between executions are positively lower bounded. Moreover, we show that the positive lower bounds of interexecution times can be enlarged by a control parameter. For a clear illustration, a practical example is given.

Event‐triggered adaptive output feedback regulation of a chain of integrators with an unknown time‐varying delay in the input

SummaryWe consider a global regulation problem for a chain of integrators with an unknown time‐varying input delay by event‐triggered output feedback control. We show that the considered system is globally regulated by the proposed event‐triggered output feedback controller with a dynamic gain‐scaling factor. Moreover, we show that interexecution times are lower bounded and these lower bounds can be increased with our control method. An example is given for clear illustration.

Adaptive Zero-order-hold Triggered Control of A Chain of Integrators with unknown Input Delay and Interexecution Time by Output Feedback

Adaptive Zero-order-hold Triggered Control of A Chain of Integrators with unknown Input Delay and Interexecution Time by Output Feedback

Periodic Event-Triggered MPC for Continuous-Time Nonlinear Systems With Bounded Disturbances

This paper is concerned with periodic event-triggering laws in robust model predictive control (MPC) for continuous-time constrained nonlinear systems. The online optimal control problem solved at triggering times is introduced. A periodic static event-triggering condition, in which a fixed sampling time interval plays an important role in avoiding Zeno behavior, is presented to alleviate continuous checking of event detections. Then a periodic dynamic event-triggering condition is investigated to further enlarge the minimal inter-execution time. Single-mode MPC with a prediction horizon larger than the control one is considered. Sufficient conditions of recursive feasibility for the online optimal control problem are derived. In order to relax the sufficient condition of stability, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ultimately Boundedness</i> properties are utilized in stability analysis. Finally, numerical simulation is provided to demonstrate the effectiveness of the proposed methods.

Adaptive event-triggered output-feedback stabilisation with double-side communication reduced for nonlinear systems with non-parametric uncertainties

This paper aims at adaptive event-triggered output-feedback stabilisation in the presence of intractable non-parametric uncertainties. Typically, double-side (i.e. sensor-to-controller and controller-to-actuator) event-triggered communication is pursued for efficient resource utilisation, unlike in related works only reducing single-side communication. This renders more constrained information transmitted via network, challenging the co-design of the compensation and event-triggering mechanisms. By incorporating a switching-varying mechanism, a distinctive adaptive event-triggered output-feedback scheme is established based on a switching filter reconstructing the unmeasurable states. Crucially, a convergence-preserving event-triggering mechanism is proposed with the adaptiveness for uncertainty compensation, by suitably exploiting the switching-varying gain. As such, a desired event-triggered output-feedback control is designed with linearity (with respect to the system output and the filter states) rendered for the controller signal. Just owing to the linearity, the controller signal is subtly kept from entering the event-triggering mechanism, so as to match the double-side event-triggered architecture. Furthermore, it is achieved that the system and filter states converge to zero while a positive minimum inter-execution time is ensured.

A New Intermittent Event-Triggered Bounded Stabilization Approach for Stochastic T–S Fuzzy Systems With External Disturbances

This article focuses on the bounded stabilization issue for stochastic Takagi–Sugeno (T–S) fuzzy systems with external disturbances under fuzzy intermittent event-triggered control. Different from the common intermittent control scheme, the intermittent control proposed is based on an event-triggered mechanism instead of a traditional time-triggered mechanism during the work intervals. As a result, it reduces unnecessary sampling times and resource waste to a great extent. Meanwhile, the minimum interexecution time is obtained for T–S fuzzy systems under the stochastic case. In addition, this article presents a novel Lyapunov function, which simplifies the proof compared to the traditional Lyapunov function for intermittent control. Based on the average control rate adopted and the Lyapunov method, a bounded stability criterion is established, which is less conservative. Then, a corollary is given under the fuzzy event-triggered control. Finally, an example is shown to illustrate the effectiveness of the results obtained.

High Minimum Inter-Execution Time Sigmoid Event-Triggered Control for Spacecraft Attitude Tracking With Actuator Saturation

This paper investigates the attitude tracking problem for spacecraft with limited communication, network congestion, unknown model parameters, actuator saturation, and external disturbances. To alleviate communication load, a novel sigmoid event-triggered mechanism is proposed with the special ability to guarantee a high minimum inter-execution time to avoid network congestion like package loss or time delay effectively. A neural network-based adaptive control algorithm is designed to deal with unknown model parameters. Besides, the problem of actuator saturation is tackled by introducing a dynamic loop gain function-based approach. System stability is proved by Lyapunov stability analysis and the high minimum inter-event time is substantiated by Zeno Behavior analysis with explanatory remarks. Numerical simulation results also show that a high minimum inter-event time and a high average inter-event time can be realized on the premise of high attitude tracking accuracy. Compared with all the previous studies, the ratio of the minimum inter-execution time to the average minimum inter-execution time has been improved by nearly 10 times with the proposed approach. Note to Practitioners—This paper was motivated by the problem of spacecraft attitude takeover control, but it also applies to other aperiodic discrete-time control systems. Existing event-triggered control methods have solved the problem of limited communication for attitude takeover control of spacecraft by reducing the number of times wireless communication is required. This paper proposes a new method for realizing quasi-periodic control with a large time gap between any two consistent control impulses using a hyperbolic tangent function or another sigmoid function in an event-triggered mechanism. The proposed sigmoid event-triggered mechanism (ETM) can magnify the event-triggered threshold dozens of times in a short time to avoid unnecessary frequent triggering without decreasing the precision of control. It’s feasible to employ the proposed sigmoid ETM to deal with limited communication and network congestion in other network control systems that are constructed with similar dynamic structures. Furthermore, it would be marvelous if we could transform this sigmoid ETM into a high-efficiency decision-making mechanism in some control systems without using a wireless network. Now we are studying how to realize orbital-attitude (maneuver) control with a relatively average time interval and fewer times of orbit transfer by using the proposed sigmoid ETM. Besides, to further improve the system performance, we are also seeking to further increase the ratio of the minimum inter-execution time to the average inter-execution time. For the purpose of a more even distribution of the triggering events on the time axis, we may modify the proposed sigmoid event-triggered method or associate it with other methods.

Event-Triggered Control of Stochastic Functional Differential Systems via Degenerate Lyapunov Functionals

This article discusses the problem of event-triggered controls (ETCs) for stochastic functional differential systems (SFDSs). For the stabilization of SFDSs, we design a proper degenerate Lyapunov functional and propose a novel ETC. The degenerate Lyapunov functional is more general than the traditional positive definitive Lyapunov functionals and ETC has a prominent advantage of reducing communication resources compared with periodic sampled-data feedback controls because time updating is based on a certain event. Also, a fixed positive lower bound on the stochastic interexecution times is guaranteed by this novel event-triggering mechanism. Together with ETC and the degenerate Lyapunov functional, the boundedness, mean square exponential stabilization, and globally asymptotical stabilization of SFDSs can be established for different choices of parameters. Finally, the obtained results are validated through numerical simulations.

Exponential synchronization of multilayer networks with white-noise-based coupling via intermittent periodic event-triggered control

In this paper, the mean-square exponential synchronization of stochastic multilayer networks with white-noise-based time-varying coupling is investigated via intermittent dynamic periodic event-triggered control. The existence of a dynamic term can reduce the number of event triggers. Furthermore, by introducing periodic sampling mechanism, a minimum inter-execution time is guaranteed to avoid Zeno phenomenon. Additionally, by employing Lyapunov method, graph theory, and stochastic analysis techniques, synchronization criteria for multilayer networks under intermittent dynamic periodic event-triggered control are established. To clarify the process of synchronization of multilayer networks, a brief framework is developed on the basis of Tajan’s algorithm. Ultimately, theoretical results are applied into Chua’s circuits and corresponding numerical simulations are given to illustrate the effectiveness and feasibility of the results.

Delay Event-Triggered Control for Stability Analysis of Complex Networks

This brief is concerned with exponential stability of delayed complex networks. Different from existing literature, an extended control is proposed, namely delay event-triggered control, in which the update of control signals is determined by the event-triggered mechanism. Both continuous event-triggered mechanism and periodic event-triggered mechanism are developed by continuous measuring and periodic sampling, respectively. The continuous event-triggered mechanism with waiting time is proposed to ensure that the existence of the minimum inter-execution time has a positive minimum value. The upper bound of the sampling period is given for the periodic event-triggered mechanism and an estimation about sampling/execution error is obtained to assess the network states. Subsequently, by employing the Lyapunov method and graph-theoretic approach, stability criteria for delayed complex networks under delay event-triggered control are established. Ultimately, the analytical results are applied into single-link robot arm systems and a corresponding numerical example is given to illustrate the effectiveness and feasibility of theoretical claims.

On robust approximate feedback linearisation with an event-triggered controller

ABSTRACT In this paper, we consider a problem of global stabilisation of approximate feedback linearised systems with perturbed nonlinearity by an event-triggered control. We categorise the perturbed nonlinearity into three cases and obtain a characterisation function for each case. Then we propose an event-triggered controller with a gain-scaling factor along with an event-triggering condition which is developed based on the characterisation function. Utilising the system analysis results, we suggest a control parameter selection rule depending on the priority on either system output regulation speed or size of the interexecution times. Via practical examples, we demonstrate the validity of our control approach.

Decentralized Dynamic Event-Triggered Adaptive Fuzzy Control for Switched Nonlinear Systems With Unstable Inverse Dynamics

In this article, the problem of decentralized dynamic event-triggered (ET) adaptive fuzzy control for a class of strong interconnected switched uncertain nonlinear systems with unstable inverse dynamics and unknown control gains is studied. By utilizing the adaptive backstepping technique and new fuzzy logic systems, decentralized ET adaptive fuzzy controllers for subsystems and a new type of switching decentralized dynamic event-triggering mechanisms are constructed. Then, the asynchronous switching problem between candidate controllers and subsystems is addressed, and the upper bound of asynchronous time is not directly restricted. Meanwhile, by ensuring that the interexecution times are lower bounded by a positive constant, Zeno behavior is avoided. Furthermore, it is proved by the multiple Lyapunov functions method that all signals in the switched closed-loop system are bounded under a new class of slow switching signals. The validity of the derived result is illustrated using two examples which include a two inverted pendulum system.

Dynamic periodic event-triggered control for input-to-state stability of multilayer coupled systems

In this article, a novel dynamic periodic event-triggered control (DPE-TC) is proposed to investigate input-to-state stability (ISS) in multilayer coupled systems (MCSs). Different from the existing literature, a dynamic term is introduced to event-triggered control (E-TC), which can reduce the number of event triggers as the interexecution times are prolonged on the whole. Moreover, a periodic sampling is adopted, from where the Zeno phenomenon is naturally avoided. Based on the Lyapunov method and graph theory, ISS for coupled systems under the DPE-TC is established. Meanwhile, a dynamic event-triggered control with dwell-time is proposed, and a corollary to ensure the ISS of MCSs is also provided. Eventually, results are applied to second-order oscillators and a numerical example is given to prove the validity of the theoretical results.

Uncertainty Compensator and Fault Estimator-Based Exponential Supertwisting Sliding-Mode Controller for a Mobile Robot.

This work proposes a novel event-triggered exponential supertwisting algorithm (ESTA) for path tracking of a mobile robot. The proposed work is divided into three parts. In the first part, a fractional-order sliding surface-based exponential supertwisting event-triggered controller has been proposed. Fractional-order sliding surface improves the transient response, and the exponential supertwisting reaching law reduces the reaching phase time and eliminates the chattering. The event-triggering condition is derived using the Lipschitz method for minimum actuator utilization, and the interexecution time between two events is derived. In the second part, a fault estimator is designed to estimate the actuator fault using the Lyapunov stability theory. Furthermore, it is shown that in the presence of matched and unmatched uncertainty, event-trigger-based controller performance degrades. Hence, in the third part, an integral sliding-mode controller (ISMC) has been clubbed with the event-trigger ESTA for filtering of the uncertainties. It is also shown that when fault estimator-based ESTA is clubbed with ISMC, then the robustness of the controller increases, and the tracking performance improves. This novel technique is robust toward uncertainty and fault, offers finite-time convergence, reduces chattering, and offers minimum resource utilization. Simulations and experimental studies are carried out to validate the advantages of the proposed controller over the existing methods.

Dynamic Deadband Event-Triggered Strategy for Distributed Adaptive Consensus Control With Applications to Circuit Systems

This paper focuses on the distributed consensus seeking of multi-agent systems (MASs) with discrete-time control updating and intermittent communications among agents. Compared with existing linearly coupled protocols, a nonlinear coupled Zeno-free event-triggered controller is first proposed, which is further to project the static and dynamic triggering mechanisms exploited by using the deadband control method. Then, the node-based nonlinear coupled adaptive event-triggered controller with online self-tuning of time-varying coupling weight and its corresponding to static and dynamic deadband-based event-triggered mechanisms are designed, respectively. The exploited adaptive event-triggered controller does not rely on any global information of interaction structure and is implemented in a fully distributed fashion. In addition, two dynamic proposals not only cover existing static strategies as special cases, but also show that the minimal inter-execution time of dynamic one is not smaller than that of static one. Theoretical analysis shows that the proposed static and dynamic deadband-based event-triggered mechanisms can not only ensure the average consensus with Zeno-freeness, but also achieve the data reduction of communication and control. Finally, the proposed algorithms applied to circuit implementation are corroborated to prove its practical merits and validity.

Event-triggered robust model predictive control with stochastic event verification

This paper is concerned with event-triggered robust model predictive control (MPC) for linear discrete-time systems with bounded disturbances. Based on the ergodicity of a purposely designed Markov chain, a stochastic triggering scheme involving a prescribed triggering function, an updating law for the transition probabilities of the Markov chain, and a checking function is proposed to achieve aperiodic and non-persistent event verification and enlarge the inter-execution time. Both tube-based MPC and linear matrix inequality-based (LMI-based) MPC are considered, and they show complementary merits with such a stochastic triggering scheme. Under mild conditions, recursive feasibility and closed-loop robust stability of both approaches are guaranteed theoretically. Simulation results are provided to show the effectiveness and merits of the proposed approaches.

Fuzzy event-triggered sliding mode depth control of unmanned underwater vehicles

This paper focuses on the problem of depth controller design of unmanned underwater vehicles (UUVs) subject to ocean currents and communication delays via a Takagi–Sugeno (T–S) fuzzy modeling method and an event-triggered integral sliding mode control strategy. An event-triggered scheme is developed to avoid unnecessary redundancy in terms of communication resources and an integral sliding mode control strategy is proposed to strength anti-interference ability of the vehicle in complex ocean currents. Sufficient conditions for the existence of a practical sliding mode and the stability of the sliding motion are established in the form of linear matrix inequalities (LMIs), under which the state trajectory is compelled to a bounded region near the sliding surface and moves along the surface toward the equilibrium point after finite time. Whether inter-execution time intervals have a positive lower bound is also analyzed and the absence of the Zeno effect in the designed event-triggered scheme is corroborated. Finally, simulation results and discussions are provided to verify the effectiveness of the new design techniques.

Stabilization Analysis for Linear Disturbed Event-Triggered Control System With Packet Losses

Based on an event-triggered control strategy, the stabilization of a linear system with disturbance is the purpose of this article. In this article, we first introduce a newfangled event-triggered control with a linear diffusive term and discontinuous sign term. Then, a class of event-triggered conditions, whose threshold contains a constant term and a sampled state term, is provided for guaranteeing the stability of a disturbed linear system. The event could be directly triggered to change the control information by violating the event-triggered condition when packet losses during control information transmission are defaulting. This means that event-triggered control can markedly economize on resource waste and communication cost. In addition, the interexecution time, which is determined by the event-triggered condition, is proved to have a uniform positive lower bound to guarantee that Zeno behavior does not occur. In the presence of packet losses, we estimate the maximum allowable number of successive packet losses to maintain the desired performance of the system. Finally, the validity of the theoretical results is substantiated by an example.