Event-triggered Control Systems Research Articles

Function observer based event-triggered control for linear systems with guaranteed L-gain

This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the difference between the current value of the system and its previously transmitted value which includes the plant output or the function observer output exceeds an additional threshold. For such an eventtriggered mechanism, we derive conditions in terms of matrix inequality to guarantee the stability as well as longer inter-event time. We propose two approaches to investigate the closed-loop model, namely, reformulating the event-triggered control system as a hybrid system and interpreting the event-induced error as exogenous disturbance. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results.

Dynamic Triggering Mechanisms for Event-Triggered Control

In this technical note, we present a new class of event triggering mechanisms for event-triggered control systems. This class is characterized by the introduction of an internal dynamic variable, which motivates the proposed name of dynamic event triggering mechanism. The stability of the resulting closed-loop system is proved and the influence of design parameters on the decay rate of the Lyapunov function is discussed. For linear systems, we establish a lower bound on the inter-execution time as a function of the parameters. The influence of these parameters on a quadratic integral performance index is also studied. Some simulation results are provided for illustration of the theoretical claims.

Event-triggered robust control for networked control systems with actuator failures and time-varying transmission delays

Purpose – The purpose of this paper is with robust control problem for event-triggered networked control systems (NCSs) with actuator failures and time-varying transmission delays. Design/methodology/approach – A random sequence is introduced to describe the actuator faults, and a novel event-triggering communication scheme is adopted in the sensor-to-controller channel. By taking the event-triggered mechanism and network transmission delay into consideration, a delay system model is constructed. Findings – Based on Lyapunov stability theory and free weighting matrix method, the feasibility criteria for co-designing both the controller gain and the trigger parameters are derived. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed linear matrix inequalities (LMIs) approach. Originality/value – The introduced approach is interesting for NCSs with actuator failures and time-varying transmission delays.

PI control synthesis for event-triggered control systems

Abstract Event-triggered control aims at reducing the resource utilization, especially the communication over the feedback link, while guaranteeing a certain control performance. Although setpoint tracking problems are common in practice, the majority of the proposed approaches in literature focus on regulation problems. Therefore, an event-triggered PI control design strategy with guaranteed performance is proposed in this paper, where both the event-triggering condition and the PI controller are implemented periodically. Based on a quadratic cost function, the PI control design problem is introduced and formulated as an LMI optimization problem. Comparisons with other approaches in the literature are made by simulation and by experimental studies to demonstrate the effectiveness of the proposed strategy.

L2 control design of event-triggered networked control systems with quantizations

This paper deals with L2 controller design problem for event-triggered networked control systems (NCSs) with quantizations. The system state is periodically sampled and quantized. A new model of NCSs that involves the network conditions, state and event-triggered communication strategy is proposed. Based on this model, some novel criteria for the asymptotic stability analysis and L2 state feedback controller design method of the event-triggered NCSs with quantizations and time-varying delay are established to guarantee a prescribed L2 disturbance rejection attenuation level γ by using Lyapunov–Krasovskii function approach. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method. It is shown that the average transmission interval could be increased substantially while the control performance is maintained.

Event-triggered control for networked control systems with quantization and packet losses

Problems of the quantized stabilization for event-triggered networked control systems (NCSs) with packet losses are addressed. To reduce the communication resources in NCSs, event-triggering scheme is adopted and designed. A NCS model is proposed which considers quantization, plant uncertainty, event-triggering scheme and packet losses simultaneously. Sufficient conditions for the stabilization and control design are derived using the Lyapunov functional approach and control synthesis of event-triggered networked control systems are established in terms of linear matrix inequalities. Moreover, the maximal allowable number of successive packet losses in NCS is estimated. A numerical example is given to illustrate the effectiveness of the proposed method.

Event-separation properties of event-triggered control systems

In this paper, we study fundamental properties of minimum inter-event times for several event-triggered control architectures, both in the absence and presence of external disturbances and/or measurement noise. This analysis reveals, amongst others, that for several popular event-triggering mechanisms no positive minimum inter-event time can be guaranteed in the presence of arbitrary small external disturbances or measurement noise. This clearly shows that it is essential to include the effects of external disturbances and measurement noise in the analysis of the computation/communication properties of event-triggered control systems. In fact, this paper also identifies event-triggering mechanisms that do exhibit these important event-separation properties.

Networked event-triggered control: an introduction and research trends

A physical system can be studied as either continuous time or discrete-time system depending upon the control objectives. Discrete-time control systems can be further classified into two categories based on the sampling: (1) time-triggered control systems and (2) event-triggered control systems. Time-triggered systems sample states and calculate controls at every sampling instant in a periodic fashion, even in cases when states and calculated control do not change much. This indicates unnecessary and useless data transmission and computation efforts of a time-triggered system, thus inefficiency. For networked systems, the transmission of measurement and control signals, thus, cause unnecessary network traffic. Event-triggered systems, on the other hand, have potential to reduce the communication burden in addition to reducing the computation of control signals. This paper provides an up-to-date survey on the event-triggered methods for control systems and highlights the potential research directions.

Event-TriggeredH∞Control for Networked Control Systems with Time-Varying Delay

This paper deals withH∞controller design problem for event-triggered networked control systems (NCSs), where the next task release time and finishing time are predicted based on the sampled states. A new model of NCSs that involves the network conditions, state, and event-triggered communication strategy is proposed. Based on this model, some novel criteria for the asymptotic stability analysis andH∞state feedback controller design of the event-triggered NCSs with timevarying delay are established to guarantee a prescribedH∞disturbance rejection attenuation level. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Event-Triggered Control Over Noisy Feedback Channels

In this paper, the stability of a discrete-time event-triggered control system over noisy feedback channels is analyzed. The transmission between the controller and the actuator is triggered by an event involving estimated control, desirable control, and a trigger threshold. It is revealed that if the trigger threshold is less than a bound determined by the system and controller matrices, then the closed-loop system is mean square stable. In addition, two equivalent conditions based on algebraic Riccati inequality/equation (ARI/ARE) are proposed to facilitate further analysis.

Stabilizing bit-rates in networked control systems with decentralized event-triggered communication

In a decentralized event-triggered networked control system (NCS), an agent samples and transmits its local state information to the controller when some local event occurs. Such event-triggered NCSs were expected to be more efficient than traditional periodically sampled system in terms of communication channel usage. This paper studies the stability of decentralized event-triggered NCS in the presence of quantization and delays. We point out some potential issues in decentralized event-triggered design and propose an alternative decentralized event with a linear-affine threshold, which avoids infinitely fast data transmission. Conditions on quantizer and communication channel are derived, which, when satisfied, can guarantee stability of the resulting NCS. Based on these conditions, finite stabilizing bit-rates are provided.

A bi-level approach for the design of event-triggered control systems over a shared network

An efficient usage of available resources is a substantial requirement for the successful design of networked control systems. Recent results indicate major benefits of event-based control compared to conventional designs, when resources such as communication, energy, and computation, are sparse. This paper considers multiple entities of heterogeneous control systems whose feedback loops are coupled through a common communication medium. The design of the decentralized event-triggering control system is formulated as an average-cost problem that aims at the minimization of a social cost criterion. A state aggregation technique is used to develop a bi-level design method, which divides into a local average-cost problem within every subsystem and a global resource allocation problem assigning optimal transmission rates to every subsystem. Stability conditions are derived that guarantee stochastic stability of the aggregate system. Under these conditions, it is shown that the design approach is asymptotically optimal as the number of subsystems increases.

On the Optimality of Certainty Equivalence for Event-Triggered Control Systems

Digital control design is commonly constrained to time-triggered control systems with periodic sampling. The emergence of more and more complex and distributed systems urges the development of advanced triggering schemes that utilize communication, computation, and energy resources more efficiently. This technical note addresses the question whether certainty equivalence is optimal for an event-triggered control system with resource constraints. The problem setting is an extension of the stochastic linear quadratic system framework, where the joint design of the control law and the event-triggering law minimizing a common objective is considered. Three differing variants are studied that reflect the resource constraints: a penalty term to acquire the resource, a limitation on the number of resource acquisitions, and a constraint on the average number of resource acquisitions. By reformulating the underlying optimization problem, a characterization of the optimal control law is possible. This characterization shows that the certainty equivalence controller is optimal for all three optimization problems.

Event-triggered guaranteed cost control for uncertain discrete-time networked control systems with time-varying transmission delays

In this study, event-triggered guaranteed cost control problem for discrete-time networked control systems (NCSs) with parameter uncertainties and time-varying transmission delays is studied. First, an event-triggering scheme for discrete-time NCSs is proposed. Then by using a delay system approach, a unified model of event-triggered control systems with parameter uncertainties and state delay is established. By applying Laypunov functional method together with linear matrix inequality (LMI) technique, sufficient conditions for the existence of an admissible guaranteed cost controller are established, which ensure a specific quadratic cost function has an upper bound for all admissible uncertainties. The proposed stability and stabilisation conditions are formulated in the framework of LMIs, which can be solved efficiently by using existing optimisation techniques. Finally, a numerical example and a practical example are given to demonstrate that, under the proposed event-triggering scheme, the advantage of reducing communication traffic in a control network without compromising the stability of the closed-loop system is preserved.

Event-triggered output feedback control for networked control systems using passivity: Achieving [formula omitted] stability in the presence of communication delays and signal quantization

When network induced delays are considered in the event-triggered control literature, they are typically delays from the plant to the network controller and a tight bound on the admissible delays is usually imposed based on the analysis of inter-event time to guarantee stability of the event-triggered control systems. In this paper, we introduce a framework for output feedback based event-triggered networked control systems (NCSs). The triggering condition is derived based on passivity theory which allows us to characterize a large class of output feedback stabilizing controllers. The proposed set-up enables us to consider network induced delays both from the plant to the network controller and from the network controller to the plant. We also take quantization of the transmitted signals in the communication network into consideration and we show that finite-gain L2 stability can be achieved in the presence of time-varying (or constant) network induced delays with bounded jitters, without requiring that the network induced delays be upper bounded by the inter-event time.

Output-Based Event-Triggered Control With Guaranteed ${\cal L}_{\infty}$-Gain and Improved and Decentralized Event-Triggering

Most event-triggered controllers available nowadays are based on static state-feedback controllers. As in many control applications full state measurements are not available for feedback, it is the objective of this paper to propose event-triggered dynamical output-based controllers. The fact that the controller is based on output feedback instead of state feedback does not allow for straightforward extensions of existing event-triggering mechanisms if a minimum time between two subsequent events has to be guaranteed. Furthermore, since sensor and actuator nodes can be physically distributed, centralized event-triggering mechanisms are often prohibitive and, therefore, we will propose a decentralized event-triggering mechanism. This event-triggering mechanism invokes transmission of the outputs in a node when the difference between the current values of the outputs in the node and their previously transmitted values becomes “large” compared to the current values and an additional threshold. For such event-triggering mechanisms, we will study closed-loop stability and L∞-performance and provide bounds on the minimum time between two subsequent events generated by each node, the so-called inter-event time of a node. This enables us to make tradeoffs between closed-loop performance on the one hand and communication load on the other hand, or even between the communication load of individual nodes. In addition, we will model the event-triggered control system using an impulsive model, which truly describes the behavior of the event-triggered control system. As a result, we will be able to guarantee stability and performance for event-triggered controllers with larger minimum inter-event times than the existing results in the literature. We illustrate the developed theory using three numerical examples.

Stabilizing bit-rate of disturbed event triggered control systems

Event triggering is a sampling method where sampling occurs only if data 'novelty' exceeds a threshold. Prior work has demonstrated that event triggered systems have longer average sampling periods than periodic sampled systems with comparable system performance. Based on this fact, it is claimed that event triggered systems make more efficient use of communication resources than periodic sampled systems. If, however, we account for the number of bits in each sample and the maximum acceptable delay of this sample, it is possible that the bit-rates generated by event triggered systems are greater than that of periodic sampled systems. Our prior work in Li et al. [2012] has established, in noise-free cases, the condition under which the stabilizing bit-rates for quantized event-triggered systems converge asymptotically to a finite rate as the system approaches its equilibrium point. In some cases, this limiting bit-rate was shown to be 0. This paper extends that earlier work to quantized event-triggered systems with essentially bounded disturbances. Conditions on triggering event, quantization error and maximum delay are established to assure the input-to-state stability (ISS). The stabilizing bit-rate is, then, shown to be always bounded by a continuous, positive definite, increasing function with respect to the norm of the state. Since the system is ISS, the stabilizing bit-rate can be bounded from above by a function of time. This result provides a guide on how to assign communication resource to the control system. If we set external disturbance to be 0, the results in Li et al. [2012] are recovered.

Event-triggered control design of linear networked systems with quantizations

This paper is concerned with the control design problem of event-triggered networked systems with both state and control input quantizations. Firstly, an innovative delay system model is proposed that describes the network conditions, state and control input quantizations, and event-triggering mechanism in a unified framework. Secondly, based on this model, the criteria for the asymptotical stability analysis and control synthesis of event-triggered networked control systems are established in terms of linear matrix inequalities (LMIs). Simulation results are given to illustrate the effectiveness of the proposed method.

Quantization Scheme Design in Distributed Event-Triggered Networked Control Systems

AbstractIn an event-triggered networked control system (NCS), an agent broadcasts its state information to its neighbors when some local event occurs. This paper studies the design of quantization scheme in such systems. We derived conditions on quantized event-triggered NCS which, when satisfied, can guarantee the asymptotic stability of the system. We also propose an event-triggered dynamic logarithmic quantizer, which fits well into the current system framework, and incurs little communication overhead.

Closed Loop Electrical Control of Urinary Continence

Individuals with spinal cord injury or neurological disorders may have neurogenic detrusor contractions at low volumes (bladder hyperreflexia), which cause incontinence and can lead to significant health problems. Bladder contractions can be suppressed by electrical stimulation of inhibitory pathways but continuous activation may lead to habituation of the inhibitory reflex and loss of continence. We determined whether conditional stimulation with electrical stimulation of inhibitory pathways applied only at the onset of nascent bladder contractions allows the bladder to fill to a greater volume before continence is lost compared with continuous stimulation. In 6 alpha-chloralose anesthetized cats cystometry was performed to compare the volume at which continence was lost under the conditions of no stimulation, continuous stimulation and conditional electrical stimulation of inhibitory pathways. PNT ENG was used to detect the onset of bladder contractions and it served as the input to an event triggered control system that regulated conditional stimulation to maintain continence. Conditional stimulation controlled by PNT ENG increased bladder capacity by 36% over no stimulation and by 15% over continuous stimulation (p <0.001 and 0.027, respectively). The event triggered control system decreased stimulation time by 67% compared to continuous stimulation. Conditional electrical stimulation of inhibitory pathways is more effective than continuous stimulation. A control system triggered by PNT ENG can maintain urinary continence.