Event-triggered Control Problem Research Articles

Distributed Event-Triggered Control for Manipulator with Fixed-Time Disturbance Observer

This article studies an event-triggered fixed-time trajectory tracking control problem of an n-joint manipulator system. Firstly, a fixed-time disturbance observer is proposed to reconstruct the total disturbance composed of external disturbances and model uncertainties, using the estimation as feedforward compensation to enhance the system robustness. Subsequently, based on the backstepping framework, a fixed-time controller with an event-triggering mechanism is designed for the manipulator to ensure the convergence of tracking errors to zero within a fixed time. Additionally, two event-triggering conditions are devised to reduce the transmission time of control input and the computation time of control output. Simultaneously, Zeno behavior is excluded through theoretical proof, validating the fixed-time stability of the closed-loop system. Finally, simulation verification is conducted on a two-joint manipulator, with results confirming the effectiveness of the control strategy.

Networked Output-Feedback MPC: A Bounded Dynamic Variable and Time-Varying Threshold-Dependent Event-Based Approach.

The event-triggered model predictive control (MPC) problem is addressed for polytopic uncertain systems. A new dynamic event-triggered mechanism (DETM) with a bounded dynamic variable and a time-varying threshold is proposed to manage measurement data packet releases. The dynamic output-feedback MPC issue is detailed as a "min-max" optimization problem (OP) with an objective function over an infinite horizon, where the hard constraint on the predictive control is required. By applying a Lyapunov-like function containing the bounded dynamic variable, an auxiliary OP constrained by several matrix inequalities is proposed, and the design methods of the output-feedback gains are provided if this auxiliary OP is feasible. The designed MPC controller ensures that the closed-loop system is input-to-state practically stable. Two examples including an event-triggered DC motor are given to illustrate the validity of the developed MPC algorithm. Simulation results verify that the proposed DETM has advantages over some existing triggering mechanisms in decreasing the consumption of resources while meeting the required performance.

Asynchronous event-triggered guaranteed cost control of uncertain 2-D Markov jump Roesser systems with actuator saturation

This paper investigates the asynchronous event-triggered guaranteed cost control problem for two-dimensional Markov jump Roesser systems with parameter uncertainties and actuator saturation. The hidden Markov model is constructed to characterize the asynchronous phenomenon induced by the mode mismatch between the system and the controller, and a hidden Markov model-based event-triggered mechanism is adopted in controller design to save communication resources. The convex hull representation is employed to process saturated inputs. By using the quadratic Lyapunov function methods and linear matrix inequality techniques, some sufficient criteria are developed to guarantee the asymptotic stability of the addressed system with a guaranteed cost under three different boundary conditions. Finally, a convex optimization algorithm with linear matrix inequality constraints is proposed to design the optimal asynchronous event-triggered guaranteed cost controller, and a numerical example is considered to demonstrate its validity.

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

Event-Triggered-Based Adaptive NN Cooperative Control of Six-Rotor UAVs With Finite-Time Prescribed Performance

This paper studies the disturbance-observer-based adaptive neural network cooperative event-triggered control problem for six-rotor unmanned aerial vehicles with finite-time prescribed performance. Six-rotor unmanned aerial vehicle systems are divided into the position subsystem and the attitude subsystem. The switching threshold event-triggered mechanism that considers the influence of event triggering on the consensus control performance is designed of each six-rotor unmanned aerial vehicle to save the transmission resources, which excludes the Zeno behavior. Neural networks are introduced for estimating the uncertainties and solving the algebraic loop problem. In addition, for the position subsystem, by combining the prescribed performance with the velocity function, a finite-time control scheme is proposed, which can guarantee that the consensus errors converge to a prespecified neighborhood of the origin, and all closed-loop signals are bounded. Based on the designed control input signal of position subsystem, an adaptive neural network event-triggered control mechanism is designed to stabilize the attitude subsystem. Finally, some verification results are given to test the rationality of the proposed control strategy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The purpose of this paper is to design an event-triggered cooperative control scheme to save the transmission resources for six-rotor unmanned aerial vehicle systems with performance limitations and lumped disturbances. In practical applications, if the impact of the event-triggered mechanism on the system performance is not taken into account, the system performance may be significantly degraded while the information transmission resource is saved. Thus, this paper designs an event-triggered mechanism that considers the system performance, which can effectively weigh the relationship between system performance and transmission resource consumption and better meet the practical requirements. Moreover, a finite-time specified performance control strategy is introduced to avoid the problem of difficult determination of residual set and improve the transient-state and steady-state performances of unmanned aerial vehicle systems, which is more in line with the actual demand.

Periodic event-triggered bipartite containment control for nonlinear multi-agent systems with input delay

ABSTRACT This paper studies the periodic event-triggered bipartite containment control problem of multi-agent systems with unmeasurable states and input delays. To deal with the system input delay problem, a Pade approximation technique is introduced. By utilising the sampled output of the system, a fuzzy state observer is constructed to estimate the unknown state. A periodic event-triggered mechanism is designed, which can effectively reduce the usage of communication resources. Compared with the traditional event-triggered control manner, a periodic event-triggered control manner only monitors the preset threshold condition at the sampling instant to determine whether to update the current control signal, which can automatically guarantee the minimum lower bound of the execution interval, avoiding the occurrence of Zeno behaviour. Stability analysis verifies that all signals in the closed-loop system are bounded, and the bipartite tracking error can converge to a small neighbourhood of the origin. Finally, a practical example further verifies the effectiveness of the designed control scheme.

Event-based adaptive secure asymptotic tracking control for nonlinear cyber–physical systems against unknown deception attacks

This article addresses the event-triggered adaptive neural network asymptotic tracking control problem for a class of nonlinear cyber–physical systems under unknown deception attacks. In the process of recursive design, a novel adaptive asymptotic tracking control strategy is proposed based on bound estimation method, backstepping technique and some smooth functions. The designed asymptotic tracking controller can ensure that the output of the system asymptotically tracks the desired signal, while ensuring that all signals in the closed-loop system are bounded. Particularly, the underlying system can be guaranteed to possess faster convergence response and higher control precision. Additionally, the Zeno behavior is ruled out. Finally, a two-stage chemical reactor is employed as an example to demonstrate the feasibility and viability of the designed control algorithm.

Periodic and Dynamic Periodic Event-Triggered Control for Nonlinear Cyber-Physical Systems Under DoS Attacks via a Hybrid System Approach

This paper is focused on the problem of periodic and dynamic periodic event-triggered control for nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks and exogenous disturbances. The analysis relies on a new model to design periodic event-triggered control and dynamic periodic event-triggered control schemes such that the nonlinear CPSs are resilient to a class of malicious attacks which can be characterized by attacking frequency and attacking duration. By developing an average dwell-time automaton and a time-ratio monitor to describe frequency and duration of the DoS attacks, general hybrid dynamical frameworks are firstly proposed for event-triggered nonlinear CPSs. Based on the established models, novel Lyapunov functions are constructed. Furthermore, thanks to the Lyapunov-based approach, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> -gain performance of the considered nonlinear CPSs under DoS attacks is analyzed. Finally, the feasibility of the theoretical findings is demonstrated by a numerical example.

Hybrid event-triggered control for networked switched Takagi–Sugeno fuzzy systems with aperiodic DoS attacks

This article investigates the event-triggered control problem for networked switched Takagi–Sugeno fuzzy systems (NSTSFSs) with denial of service (DoS) attacks. First, an attack-instant-constrained hybrid event-triggered mechanism (ETM) is proposed, which uses the acknowledgment character (ACK) detection scheme. It can describe the triggering schemes under different attack intervals and modify the triggering frequency based on the performance of the system. Second, a new segmented Lyapunov function is designed that takes into account the asynchronous behavior of system and controller modes, as well as DoS frequency and duration constraints. Then, sufficient conditions are provided to ensure the exponential stability of the system and have an H∞ performance. Furthermore, a collaborative design scheme is proposed to obtain controller gains, the switching law, and event-triggered parameters. Finally, the accuracy and effectiveness of this method are verified through two simulation examples.

Neural-network-based adaptive control of strict-feedback nonlinear systems with actuator faults: Event-triggered communications strategy

This article considers the neural network-based event-triggered adaptive control problem for a class of strict-feedback nonlinear impulsive systems with actuator faults and external disturbances. It is well known that reducing computational resources and carrier loads is a long-standing task in the field of adaptive control. However, the event-triggered scheme used in traditional research still consumes relatively more resources. To solve the problem, the control scheme in this paper only updates the controller and weight parameters at the event-triggered moments. Dedicated efforts are made to certificate the stability of the system through a new Lyapunov theory, in such a way that the system maintains its stability well even under uncertainties. Finally, two emulation examples are exploited to demonstrate the efficacy and applicability of the proposed approach.

Fixed-time adaptive event-triggered control for multiagent systems with full-state constraints

This paper investigates the fixed-time adaptive event-triggered control problem for a class of nonlinear multiagent systems with full-state constraints. The problem of full-state constraints is solved for multiagent systems by utilising a one-to-one nonlinear mapping. The design conditions of the controllers are more easily satisfied than the existing barrier Lyapunov functions strategy. A fixed-time adaptive control scheme is proposed for unconstrained systems that are converted from constrained systems. In contract with the existing finite-time control schemes that rely on the initial states, this restriction condition can be removed in this paper. An improved event-triggered mechanism with an adaptable switching threshold is designed to provide flexible switching between fixed threshold and variable threshold policies, resulting in reduced execution and sampling. It is proved via the Lyapunov stability method that all signals of the closed-loop systems are semi-global practical fixed-time stable. Finally, the effectiveness of the proposed control strategy is verified by some simulation results.

A Multifilters Approach to Adaptive Event-Triggered Control of Uncertain Nonlinear Systems With Global Output Constraint.

This article focuses on the problem of adaptive event-triggered output feedback control for a class of uncertain nonlinear systems under the output constraint. Different from the existing works, the time-varying parameters and the global output constraint are taken into account. First, by means of multifilters, the unmeasurable state variables are reconstructed, under which the unknown time-varying parameters and sensor sensitivity are transformed into the estimation problem of unknown parameters. Second, based on a barrier function, a novel constraint algorithm is established to make the output enter into asymmetric time-varying constraint boundaries, which is independent of the initial value of the output. To avoid continuous sampling of the controller, an event-triggered mechanism is proposed without the Zeno phenomenon. By means of the Lyapunov stability theory, it is strictly proved that the output enters into the pregiven asymmetric constraint boundaries, and never exceeds. Finally, the validity of our proposed control algorithm is illustrated by a numerical simulation.

Event-triggered adaptive leaderless consensus control for nonlinear multi-agent systems with unknown dead-zones and output constraints

This article investigates the event-triggered adaptive control problem for a class of leaderless multi-agent systems with output constraints and unknown dead-zones. The adaptive updating laws are designed to eliminate the effects of unknown dead-zones by employing adaptive backstepping technique. The barrier Lyapunov function (BLF) is introduced to guarantee that the output constraints are not violated. Then, a generalized relative threshold is proposed by utilizing the neighboring controller errors to alleviate the computation burden dramatically. It is further shown that all the closed-loop signals are uniformly bounded and that the consensus tracking errors asymptotically tend to zero. A simulation example verifies the validation of the developed control strategy.

Event-Triggered Adaptive Control for a Class of Nonlinear Systems with Dead-Zone Input

In this paper, the event-triggered control problem is investigated using backstepping techniques for nonlinear systems with dead-zone input. The external disturbance and unknown parameters are also considered in the controller’s design. It is well known that errors in input signal measurements are inevitable. In event-triggered control, such errors will directly affect whether the control signal is updated. This measurement error can be seen in the form of interference to the threshold. Therefore, unlike traditional event-triggered control, the existence of threshold disturbance is considered in the controller’s design. The proposed controller can not only compensate for the uncertainties caused by external disturbance and unknown parameters but can also suppress the unknown effects caused by threshold interference. In addition, to obtain a continuous controller, a smooth function is constructed to approximate the discontinuous sign function. In this way, Zeno behavior is successfully avoided. The boundedness of all signals and the tracking performance of the system can be guaranteed by the proposed control scheme. Numerical simulation and actual system simulation demonstrate the effectiveness of the proposed control scheme. The comparative simulation results also verify this event-triggered controller’s advantages, including better tracking performance and fewer trigger times.

A New Event-Triggered Adaptive Fixed-Time Control Design for Uncertain Nonlinear Systems.

This article investigates the problem of dynamic memory event-triggered (DMET) fixed-time tracking control within time-varying asymmetric constraints for nonaffine nonstrict-feedback uncertain nonlinear systems with unmodeled dynamics and unknown disturbances. The existing dynamic event-triggered control methods cannot handle the nonlinear systems with unmodeled dynamics and nonaffine inputs, which greatly limits the applicability of the strategy. To this end, a novel DMET adaptive fuzzy fixed-time control protocol is constructed based on the idea of command filtered backstepping, in which a new dynamic signal function is established to deal with the unmodeled dynamics and an improved DMET mechanism (DMETM) is designed to solve the problem of nonaffine inputs. It is proved that the newly DMET control strategy ensures the tracking error converges to an arbitrarily small compact set in a fixed time and all the signals of the closed-loop systems are bounded. The effectiveness of the proposed approach is demonstrated by two simulation examples.

Mixed-Zero-Sum-Game-Based Memory Event-Triggered Cooperative Control of Heterogeneous MASs Against DoS Attacks.

This article studies the problem of memory event-triggered cooperative adaptive control of heterogeneous nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks based on the multiplayer mixed zero-sum (ZS) game strategy. First, a neural-network-based reinforcement learning scheme is structured to obtain the Nash equilibrium solution of the proposed multiplayer mixed ZS game scheme. Then, a memory-based event-triggered mechanism considering the historical data is proposed. This effectively avoids incorrect triggering information caused by unknown external factors. Moreover, thanks to the idea of switching topology, the mixed ZS game problem under the influence of node-based DoS attacks is solved efficiently. In accordance with the Lyapunov stability theory, it is proved that all signals of heterogeneous MASs are bounded, all heterogeneous followers can track the trajectory of the leader during the no-attack period, the attacked follower can achieve stabilization control during the attack period, and the remaining nonattacked followers can achieve cooperative control during the attack period. Finally, the effectiveness of the designed memory-event-triggered-based mixed ZS game cooperative control strategy is tested by the given simulation results.

Event-Triggered Boundary Control of Semilinear Hyperbolic Systems

We present an event-triggered boundary control scheme for hyperbolic systems. The trigger condition is based on predictions of the state on determinate sets, and the control input is updated only when the predictions deviate from the reference by a given margin. Nominal closed-loop stability, the absence of Zeno behaviour, and robustness to uncertainty and disturbances, are all established analytically. For the special case of linear systems, the trigger condition can be expressed in closed-form as an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> -scalar product of kernels with the distributed state. The presented controller can also be combined with existing observers to solve the event-triggered output-feedback control problem. A numerical simulation demonstrates the effectiveness of the proposed approach.

Global Event-Triggered Funnel Control of Switched Nonlinear Systems via Switching Multiple Lyapunov Functions.

In this article, the global event-triggered (ET) funnel tracking control problem is studied for a class of switched nonlinear systems with structural uncertainties, where the solvability of the control problem for each subsystem is not needed. A switching multiple Lyapunov functions (MLFs) method is established, where MLFs are designed to handle switched inverse dynamics, and a switching barrier Lyapunov function is constructed to address switched sampled errors that may compromise system stability. This is achieved alongside a new switching dynamic event-triggering mechanism (DETM). By combining this method with backstepping, a dwell-time state-dependent switching law and an ET funnel controller of each subsystem are constructed, effectively eliminating the issue of the "explosion of complexity" encountered in traditional backstepping without using dynamic surface control or command filters. Additionally, the designed switching DETM ensures that the tracking error always evolves within a performance funnel in any consecutive triggering interval, excluding Zeno behavior, and guaranteeing positive constant lower bounds for two consecutive triggering intervals and any switching interval, respectively. Finally, an example is provided to show the validity of the theoretical results.

A Novel Dual-Phase Based Approach for Distributed Event-Triggered Control of Multiagent Systems With Guaranteed Performance.

This article presents a novel dual-phase based approach for distributed event-triggered control of uncertain Euler-Lagrange (EL) multiagent systems (MASs) with guaranteed performance under a directed topology. First, a fully distributed robust filter is designed to estimate the reference signal for each agent with guaranteed observation performance under continuous state feedback, which transforms the distributed event-triggered control problem into a centralized one for multiple single systems. Second, an event-triggered controller is constructed via intermittent state feedback, making the output of each agent follow the corresponding estimated signal with guaranteed tracking performance. The proposed co-design scheme is of relatively low complexity in structure and cheap in computation since a priori knowledge of system nonlinearities or estimation of their bounds is not required in building the control scheme, and yet neither approximating structures nor adaptive online updating algorithms are needed. It is shown that the output tracking error of each agent is ensured to shrink into a prescribed precision set at an arbitrarily assignable convergence rate, although the plant states and the actuation signal are triggered simultaneously. All the internal signals are uniformly bounded and the occurrence of Zeno behavior is precluded. The efficiency of the proposed method is verified via numerical simulation.

An analytical approach to finite time H∞ event-triggered state feedback control of fractional order systems with delay

This paper investigates finite time H∞ event-triggered state feedback control problem of fractional-order systems with delay. Based on Laplace trasform and “inf-sup” norm, a delay-dependent sufficient condition for designing H∞ event-triggered control is established in terms of the Mittag-Leffler function and Linear matrix inequalities. A numerical example is given to show the effectiveness of the obtained result.