Event-triggered Control For Nonlinear Systems Research Articles

Adaptive finite-time event-triggered control for nonlinear systems with quantized input and periodic disturbances

Adaptive finite-time event-triggered control for nonlinear systems with quantized input and periodic disturbances

Safety-critical event-triggered control of nonlinear systems with tunable input-to-state safe barrier functions

This paper investigates safety-critical event-triggered control (ETC) for nonlinear systems. It proposes a new ETC strategy that ensures event-triggered safety by using a tunable input-to-state safe barrier function. Then, a method is devised to effectively save communication resources and reduce computational load through the construction of a suitable dynamic event-triggered mechanism. Furthermore, the exclusion of Zeno behavior is guaranteed for the closed-loop system. Finally, this paper culminates by presenting two illustrative examples that showcase the effectiveness of proposed control strategies.

Dynamic periodic event-triggered control for nonlinear systems with output dynamic quantization

This paper is concerned with the design of stabilizing event-triggered controllers for nonlinear systems subject to dynamic quantization. The plant state is assumed to be partially known, and the feedback signal is transmitted to the controller at discrete-time instants via a digital channel. To that end, an event-triggered controller is synthesized based solely on the available plant measurement. In addition, to better adapt it to practical implementation, the event-triggering law we construct is only verified at periodic time instants, i.e., periodic event-triggering mechanism. Since the network is digital, the transmitted output signal must be quantized to be encoded using a finite number of bits. Furthermore, the initial output value is assumed to be unknown, and the plant is affected by external disturbance, which can result in quantizer saturation. To overcome these challenges, a dynamic quantization policy is developed for the output measurement such that the quantization regions are dynamically updated according to the value of the quantized signal. The combined approach of periodic event-triggering mechanism and dynamic quantization ensures the stability of the networked control system under mild conditions. The stability is studied using appropriate Lyapunov functions. Numerical simulations have been conducted to justify the proposed technique.

Event-Triggered Control for Nonlinear Systems With Center Manifolds

Event-Triggered Control for Nonlinear Systems With Center Manifolds

Asynchronous robust fuzzy event-triggered control of nonlinear systems

This paper deals with the problem of event-triggered integral sliding mode control (ISMC) for the perturbed nonlinear based-Takagi-Sugeno (TS) fuzzy systems. To reduce the chattering introduced by the unmatched disturbances, a disturbance observer is designed to get the estimated unmatched disturbances. To further reduce the computational burden and communication resources, compared with previous studies, two types of sliding surfaces are established. The time-triggered-based sliding surface which is used to ensure the reachability of the system states and the event-triggered-based sliding surface that is presented to calculate the control law, directly which benefits from less updates and consequently, less chattering that enhance the system performance. Moreover, the suggested control scheme is proposed based on asynchronous trait, i.e., the premise variables of the controller are in different time scale with the fuzzy systems which also leads to communication resource reduction. As a key issue in event-triggered control, it is ensured that the proposed controlled system is Zeno-free along the implementation. By the Lyapunov theory, the appropriate conditions for the ultimate boundedness stability (UBS) of the closed-loop system with a prescribed H∞ performance are derived in new offline LMIs. In order to illustrate the effectiveness of the suggested event-triggered integral sliding mode control, the Rossler system and track-trailer system are simulated and the obtained results are evaluated with the existing methods.

Adaptive Event-Triggered Control for Nonlinear Systems With Asymmetric State Constraints: A Prescribed-Time Approach

Finite/Fixed-time control yields a promising tool to optimize a system&#x0027;s settling time, but lacks the ability to separately define the settling time and the convergence domain (known as <i>practically prescribed-time stability</i>, PPTS). We provide a sufficient condition for PPTS based on a new piecewise exponential function, which decouples the settling time and convergence domain into separately user-defined parameters. We propose an adaptive event-triggered prescribed-time control scheme for nonlinear systems with asymmetric output constraints, using an exponential-type barrier Lyapunov function. We show that this PPTS control scheme can guarantee tracking error convergence performance, while restricting the output state according to the prescribed asymmetric constraints. Compared with traditional finite/fixed-time control, the proposed methodology yields separately user-defined settling time and convergence domain without the prior information on disturbance. Moreover, asymmetric state constraints can be handled in the control structure through bias state transformation, which offers an intuitive analysis technique for general constraint issues. Simulation and experiment results on a heterogeneous teleoperation system demonstrate the merits of the proposed control scheme.

Improved Dynamic Event-Triggered Control for Nonlinear Systems with Fading Channels

This paper is devoted to the protocol-based control design for nonlinear systems with fading channels. Distinguished from the existing event-triggering criteria associated with only two consecutive packets, an improved dynamic event-triggered protocol is formulated, which accounts for some historical available transmitted packets. As a consequence, the number of triggering times can be reduced efficiently while maintaining desired control performance. Meanwhile, the time-varying fading channel is described by a Markov process within finite space, whose mode can be detected via a hidden Markov mode detector. Based on Lyapunov stability theory, sufficient conditions are derived to achieve the stochastic stability of the closed-loop system. In the end, the validity of the derived results is verified through an application study.

Computing the average inter-sample time of event-triggered control using quantitative automata

Event-triggered control (ETC) is a major recent development in cyber–physical systems due to its capability of reducing resource utilization in networked devices. However, while most of the ETC literature reports simulations indicating massive reductions in the sampling required for control, no method so far has been capable of quantifying these results. In this work, we propose an approach through finite-state abstractions to do formal quantification of the traffic generated by ETC of linear systems, in particular aiming at computing its smallest average inter-sample time (SAIST). The method involves abstracting the traffic model through l-complete abstractions, finding the cycle of minimum average length in the graph associated to it, and verifying whether this cycle is an infinitely recurring traffic pattern. The method is proven to be robust to sufficiently small model uncertainties, which allows its application to compute the SAIST of ETC of nonlinear systems.

Recent Developments in Event-Triggered Control of Nonlinear Systems: An Overview

Event-triggered control is a most popular paradigm for transferring feedback information in an economical “as needed” manner. The study of event-triggered control can be traced back to the 1960s. Following significant advances on the topic of control over networks and the topic of nonlinear control systems over the last two decades, event-triggered control has quickly emerged as a major theoretical subject in control theory. Applications of event-triggered control are wide-spread ranging from embedded control systems and industrial control processes to unmanned systems and cyber-physical transportation networks. In this paper, we first review developments in the synthesis of event-triggered sampling mechanisms. Various event triggering mechanisms, such as static event trigger, dynamic event trigger, time-regularized event trigger, and event trigger with positive threshold offsets, are systematically discussed. Then, we study how to design a stabilizing controller that is robust with respect to the sampling errors. Finally, we review some recent results in the directions of self-triggered control, event-triggered tracking control and cooperative control, and event-triggered control of stochastic systems and partial differential equation systems. Practical applications of event-triggered control are also discussed.

Event-triggered control for nonlinear systems involving hybrid impulses

In this paper, we apply event-triggered control to nonlinear systems with impulses, and investigate the problem of ensuring globally exponential stability (GES) of the systems, where events and impulses may occur at different time. Moreover, two types of impulses (i.e., stabilizing and destabilizing) can coexist. On the basis of Lyapunov method and impulsive control theory, some sufficient conditions ensuring GES are derived, and the Zeno behaviour can be excluded. These conditions are presented in the form of linear matrix inequalities (LMI). In particular, inspired by average dwell-time methods, conditions for restriction of impulses are proposed, which guarantee GES of nonlinear systems involving single stabilizing and destabilizing or multiple impulses, respectively. Furthermore, the problem of designing event-triggered mechanism and control gains are solved by using LMI method. Lastly, two numerical simulation examples are given to represent the effectiveness of our results.

Periodic decentralized event-triggered control for nonlinear systems with asynchronous update and dynamic quantization

Periodic decentralized event-triggered control for nonlinear systems with asynchronous update and dynamic quantization

Safety-critical dynamic event-triggered control of nonlinear systems

This paper is concerned with the problem of safety-critical dynamic event-triggered control (ETC) for nonlinear systems. A novel safety-critical dynamic ETC strategy is proposed to simultaneously guarantee event-triggered safety and stability based on the union of input-to-state safe barrier function (ISSf-BF) and input-to-state stable Lyapunov function (ISS-LF). Also, an appropriate dynamic event-triggered mechanism (DETM) is constructed, and Zeno phenomenon of ETC in the safety-critical control framework is definitely excluded based on the DETM constructed. Compared with the existing safety-critical control designed in the framework of continuous-time feedback control, the proposed strategy constructs safety-critical event-triggered controller and an DETM, which greatly alleviates the unnecessary waste of communication and computation resources. Finally, three examples are presented to demonstrate the effectiveness of the proposed design strategy.

Predictor-based Event-triggered Control of Nonlinear Systems with State and Input Delays

Predictor-based Event-triggered Control of Nonlinear Systems with State and Input Delays

Event-triggered control for nonlinear systems with impulse effects

This paper studies the exponential stability of nonlinear systems involving impulse effects based on event-triggered control, where the impulsive sequence is generated by some well-designed event conditions. On one hand, from the impulsive disturbance point of view, some sufficient conditions are derived based on event-triggered sampled-data control with the help of linear matrix inequalities (LMIs) method, where the control effects of sampled-data control and negative effects of impulses are fully considered. On the other hand, from the impulsive control point of view, some LMI-based conditions are presented based on event-triggered hybrid control, i.e., event-triggered sampled-data control and impulsive control, where a class of forced impulses is introduced to reduce the conservatism of the control strategy. The control gains of sampled-data control and impulsive control can be easily designed via our designed LMI conditions. Moreover, the Zeno behaviour can be excluded in our results. Finally, two numerical examples are presented to illustrate the validity of our control strategies.

Event-Triggered Control of Nonlinear Systems With Time-Varying State Delays

Nonlinear systems with time delays have been object of intense investigation in the last decades for their ability of capturing the behavior of many natural and engineering systems, including ecological, biomedical, industrial, robotic, and networked systems. In this article, a method for the event-triggered stabilization in the sample-and-hold sense of nonlinear time-delay systems with time-varying state delays is presented. The approach exploits control Lyapunov-Razumikhin functions and a spline-based approximation of the functional state feedback, resulting in a finite-memory controller that avoids (by construction) continuous-state monitoring while ensuring also that the minimal interevent time is strictly positive. Examples of application of the illustrated technique highlight the potential of the approach taken.

Output-Based Periodic Event-Triggered Control for Nonlinear Plants: An Approximate-Model Method

This article studies periodic event-triggered control for nonlinear systems with multiple outputs and disturbances. First, an approximate-model method is introduced to discretize nonlinear plants with a family of controllers parameterized by verification periods. Then, a novel summation-based event-triggering condition is designed to ensure input-to-state practical stability of closed-loop systems. It is shown that the proposed event-triggering condition can admit a positive lower bound of interevent times for a family of controllers. Furthermore, an improved event-triggering condition is given to maximize the ranges of allowable parameters. Finally, numerical simulations are provided to illustrate the efficiency and feasibility of the obtained results.

Event-triggered control for nonlinear systems via feedback linearisation

This paper focuses on the problem of event-triggered control for nonlinear systems via feedback linearisation. In the design procedure, the static event-triggered mechanisms and dynamic event-triggered mechanisms are applied to deal with nonlinear systems via feedback linearisation. Two cases of feedback linearisation are discussed. Besides, we prove that these two triggering mechanisms guarantee that all the closed-loop signals are asymptotically stable. The effectiveness of the proposed methods is illustrated and compared using simulation examples.

Measurement feedback control of nonlinear systems: a small-gain approach

This paper presents a new tool for feedback control design of nonlinear systems in the presence of non-smooth measurement errors. We introduce a small-gain design approach to robust control of nonlinear uncertain systems with disturbed measurement. As a design ingredient, a modified gain assignment technique for measurement feedback control of nonlinear uncertain systems is proposed. Through a recursive control design approach, the closed-loop system is transformed into a network of input-to-state stable (ISS) systems and the influences of the measurement errors are represented by ISS gains. The feedback control objective is achieved by applying the cyclic-small-gain theorem to the closed-loop system. Moreover, event-triggered control of nonlinear systems is studied in a unified framework of measurement feedback control.

Event-Triggered Control of Nonlinear Systems With Updating Threshold

In this letter, the problems of event-triggered and self-triggered control of nonlinear systems are addressed. In particular, by exploiting certain stability assumptions for the continuous-time system as well as the Lipschitz properties of the system’s dynamics, strategies are presented that guarantee the stability of the sampled closed-loop system. By enforcing an updating threshold strategy, at each event instant, the controller is updated to preserve the system’s stability properties, while the triggering mechanism is also updated which may reduce future controller updates.

Observer-Based Event-Triggered Control for Nonlinear Systems With Mixed Delays and Disturbances: The Input-to-State Stability.

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.