Periodic Event-triggered Control Research Articles

Energy-Efficient Control for an Unmanned Ground Vehicle in a Wireless Sensor Network

In this paper, an energy-efficient control solution for an Unmanned Ground Vehicle (UGV) in a Wireless Sensor Network is proposed. This novel control approach integrates periodic event-triggered control, packet-based control, time-varying dual-rate Kalman filter-based prediction techniques, and dual-rate control. The systematic combination of these control techniques allows the UGV to track the desired path preserving performance properties, despite (i) existing scarce data due to the reduced usage of the wireless sensor device, which results in less number of transmissions through the network and, hence, bandwidth and battery saving; (ii) appearance of some wireless communication problems such as time-varying delays, packet dropouts, and packet disorder; and (iii) coping with a realistic scenario where external disturbance and sensor noise can arise. The main benefits of the control solution are illustrated via simulation.

Traffic Models of Periodic Event-Triggered Control Systems

Periodic event-triggered control (PETC) is a version of event-triggered control (ETC) that only requires to measure the plant output periodically instead of continuously. In this work, we present a construction of timing models for these PETC implementations to capture the dynamics of the traffic they generate. In the construction, we employ a two-step approach. We first partition the state space into a finite number of regions. Then in each region, the event-triggering behavior is analyzed with the help of LMIs. The state transitions among different regions result from computing the reachable state set starting from each region within the computed event time intervals.

Periodic Event-Triggered Control for Nonlinear Networked Control Systems

Periodic event-triggered control (PETC) is an appealing paradigm for the implementation of controllers on platforms with limited communication resources, a typical example being networked control systems. In PETC, transmissions over the communication channel are triggered by an event generator, which depends solely on the available plant and controller data and is only evaluated at given sampling instants to enable its digital implementation. In this paper, we consider the general scenario, where the controller communicates with the plant via multiple decoupled networks. Each network may contain multiple nodes, in which case a dedicated protocol is used to schedule transmissions among these nodes. The transmission instants over the networks are asynchronous and generated by local event generators. At given sampling instants, the local event generator evaluates a rule, which only involves the measurements and the control inputs available locally, to decide whether a transmission is needed over the considered network. Following the emulation approach, we show how to design local triggering generators to ensure input-to-state stability and $\mathcal {L}_p$ stability for the overall system based on a continuous-time output-feedback controller that robustly stabilizes the network-free system. The method is applied to a class of Lipschitz nonlinear systems, for which we formulate the design conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example.

Adaptive fuzzy guaranteed performance control for uncertain nonlinear systems with event-triggered input

This paper investigates the issue of event-triggered adaptive tracking control for a class of nonlinear systems with unmeasurable states and uncertain nonlinearities. A state observer based on fuzzy logic systems (FLSs) is first established for further stability analysis. Under the framework of backstepping technique, a novel adaptive backstepping control scheme is proposed, where the controller updates are event-driven to decrease the communication burden between the plant and the controller. Differing from the existing results for periodic event-triggered control (ETC), the proposed event-triggered strategy is aperiodic, which depends on the measurement errors with respect to fixed threshold and the magnitude of control signal. Especially, it should be mentioned that the discontinuous control signals in ETC might bring poor transient performance. Therefore, the prescribed performance bounds (PPBs) method with barrier Lyapunov function is utilized to balance the system performance and the number of triggering events. Finally, it is proved that all closed-loop signals can converge to a desired compact set and the output tracking error is within the specified bounds. Simulation example illustrates the effectiveness of the proposed control scheme.

Periodic Event-Triggered Dynamic Output Feedback Dissipative Control With Stochastic Detection

This brief is concerned with the problem of periodic event-triggered dynamic output feedback (DOF) dissipative control with a probabilistic detection of event-triggering conditions. By employing the input-delay approach, the stochastically periodic event-triggered control (SPETC) system is modeled as a probabilistic delay closed-loop system. Then by utilizing tools from Lyapunov functional and stochastic system theory, sufficient conditions are derived in terms of linear matrix inequalities to guarantee the closed-loop system to be strictly $(\mathcal {Q}, \mathcal {S}, \mathcal {R})$ - $\alpha $ -dissipative. The effectiveness of the design procedure is illustrated numerically by conducting simulations on a second order series RLC circuit example.

Periodic Event-Triggered Control strategy for a (3,0) mobile robot network

This work deals with the development of a nonlinear Periodic Event-Triggered Control strategy employed to the consensus of a multi-vehicle autonomous system based on (3,0) mobile robots. First, the existence of the Control Lyapunov Function (CLF) applicable to the consensus problem is proven. This is subsequently used to develop event and feedback functions. The Periodic Event-Triggered Control ensures trajectories boundedness and convergence to consensus while a specific sampling period is provided. Also, the formation problem is addressed as an extension of the presented work. Experimental results show the performance of the proposed control strategy which reduces 99.78% the number of control updates compared to a continuous control law, resulting in energy saving for the information transfer from central control to the mobile robots.

Dynamic event-triggered control for linear stochastic systems with sporadic measurements and communication delays

This paper deals with the stability of linear stochastic systems in the presence of sporadic measurements and communication delays. Motivated by considerations about the efficient use of the available resources, two so-called dynamic discrete-time event-triggered control (DTETC) strategies tailored to the system are designed, including some existing periodic event-triggered control strategies as particular cases. An impulsive switched system approach and a switched time-delay system approach are developed for modeling and stability analysis of the resulting closed-loop systems, respectively. In addition, it is shown that under the same decay rate, the designed dynamic DTETC may further reduce the conservatism than their static counterparts. Interestingly, the proposed impulsive switched system approach can capture the stabilizing effect of the communication delays. A numerical example is provided to illustrate the theoretical results.

Periodic event-triggered control for networked control systems based on non-monotonic Lyapunov functions

This article considers exponential stabilization of linear Networked Control Systems with periodic event-triggered control for a given network specification in terms of a maximum number of successive dropouts and a constant transmission delay. Based on stability results using non-monotonic Lyapunov functions for discontinuous dynamical systems, two sufficient results for stability of the general model of a linear event-triggered Networked Control System are derived. Those results are used to derive robust periodic event-triggered control strategies. First, a static triggering mechanism for the case without delay is derived. Afterwards, two dynamic triggering mechanisms are developed for the case without and with delay. It is shown how a degree of freedom, being contained in the dynamic triggering mechanisms, can be used to shape the resulting network traffic. The applied adaption technique is motivated by existing congestion control mechanisms in communication networks. The properties of the derived mechanisms are illustrated in a numerical example.

A Periodic Event-Triggered Design of Robust Filtering for T-S Fuzzy Discrete-Time Systems.

Periodic event-triggered control (PETC) is a control strategy consisting of event-triggered control (ETC) and conventional periodic sampled-data control. By using event-triggering mechanisms (ETM) to periodically verify whether or not to transmit and compute the measured output, communication and computational datum are significantly reduced while still retaining a satisfactory performance. This paper investigates the PETC scheme of robust ∞ filtering for a class of uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems, where the sample time is assumed to be a constant. To analyze the filtering problems of the PETC strategy, we present two frameworks based on perturbed linear and piecewise linear systems, to model filtering error systems. Sufficient conditions for the existence of a robust ∞ filter are derived in the form of matrix inequalities (LMIs) under these two frameworks, respectively. Finally, a simulation example is used to testify to the effectiveness of the proposed approach.

Explicit Computation of Sampling Period in Periodic Event-Triggered Multiagent Control Under Limited Data Rate

This paper investigates the coordination of nonlinear sampled-data multiagent systems subject to a data rate constraint. The purpose is to design resource-efficient communication and control strategies that guarantee exponential synchronization. Two implementation scenarios are considered: the period time-triggered control and the period event-triggered control. One of the main difficulties of the problem is to obtain an explicit formula for the maximum-allowable sampling period (MASP). To this end, an approach on finding the MASP for period time-triggered control is proposed first. Then, an asynchronous period event-triggered control strategy is formulated, and a communication function and a control function are designed for each agent to determine, respectively, whether the sampled state and control input should be transmitted at each sampling instant. Finally, the constraint of the limited data rate is considered. An observer-based encoder–decoder and a finite-level quantizer are designed, respectively, for the sensor-controller communication and the controller-actuator communication such that a certain constraint on the data rate is satisfied. It is shown that exponential synchronization can still be achieved in the presence of the data-rate constraint. A simulation example is given to illustrate the effectiveness of the theoretical results.

Periodic event-triggered dynamic output feedback control of switched systems

This paper considers the problem of co-design of a dynamic output feedback controller and a periodic event-triggering mechanism for control of switched systems under limited communication resources. The dynamic output feedback controller is designed to utilize quantized output measurements which can reduce the load on communication; a logarithmic quantizer model is assumed. The event-triggering mechanism is designed to detect events periodically which can significantly reduce sampling frequency and preclude the occurrence of Zeno behavior due to continuous-time sampling. The governing equations of the physical system combined with the equations of the dynamic output feedback controller and the event-triggering mechanism are formulated as a switched delay system. For the closed-loop switched delay system, sufficient conditions in terms of Linear Matrix Inequalities (LMIs) are obtained to achieve exponential stability with a prescribed L2−L∞ attenuation performance with respect to an exogenous disturbance; both weighted and non-weighted performance can be achieved with the proposed approach. Tools and techniques from delay-dependent Lyapunov theory, free-weighting matrices, Singular Value Decomposition (SVD), and average dwell time for switched systems are used to obtain the main results. A synthesis procedure is provided for obtaining the dynamic output feedback controller gains, event-triggering condition parameters, and a lower bound on the average dwell time of the switching signal. Numerical simulation results on a switched boost converter circuit system are provided to evaluate the proposed design and results.

Periodic event-triggered resilient control for cyber-physical systems under denial-of-service attacks

This paper studies the problem of designing a resilient control strategy for cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. By constructing an H∞ observer-based periodic event-triggered control (PETC) framework, the relationship between the event-triggering mechanism and the prediction error is obtained. Then, inspired by the maximum transmission interval, the input-to-state stability of the closed-loop system is proved. Compared with the existing methods, a Zeno-free periodic PETC scheme is designed for a continuous-time CPS with the external disturbance and measurement noise. In particular, the objective of maximizing the frequency and duration of the DoS attacks is achieved without losing robustness. Finally, two examples are given to verify the effectiveness of the proposed approach.

Periodic event-triggered robust output feedback control for nonlinear uncertain systems with time-varying disturbance

This paper investigates the periodic event-triggered robust output feedback control problem for a class of nonlinear uncertain systems subject to time-varying disturbance. By means of the feedback domination approach and disturbance compensation technique, a new framework of periodic event-triggered robust control strategy is developed in the form of output feedback, which encompasses a discrete-time event-triggering transmission scheme that is only intermittently monitored at sampling instants and a discrete-time output feedback controller consisting of a set of linear difference equations. The proposed robust method may reduce the communication resource utilization as compared to the non-event triggering schemes while maintaining a desirable closed-loop system performance even in the presence of a general class of time-varying disturbance and nonlinear uncertainties. The closed-loop system under the proposed control scheme is actually modeled as a hybrid system, and it is shown that the global practical stability of the closed-loop hybrid system is guaranteed by selecting a sufficiently large scaling gain and a sufficiently small sampling period. Finally, the experimental results on a DC–DC buck power converter are presented to illustrate the effectiveness of the proposed control approaches.

Decentralized periodic event-triggered control with quantization and asynchronous communication

Asynchronous decentralized event-triggered control (ADETC) Mazo Jr. and Cao (2014) is an implementation of controllers characterized by decentralized event generation, asynchronous sampling updates, and dynamic quantization. Combining those elements in ADETC results in a parsimonious transmission of information which makes it suitable for wireless networked implementations. We extend the previous work on ADETC by introducing periodic sampling, denoting our proposal asynchronous decentralized periodic event-triggered control (ADPETC), and study the stability and L2-gain of ADPETC for implementations affected by disturbances. In ADPETC, at each sampling time, quantized measurements from those sensors that triggered a local event are transmitted to a dynamic controller that computes control actions; the quantized control actions are then transmitted to the corresponding actuators only if certain events are also triggered for the corresponding actuator. The developed theory is demonstrated and illustrated via a numerical example.

Non-uniform Multi-rate Estimator based Periodic Event-Triggered Control for resource saving

This paper proposes a systematic non-uniform multi-rate estimation and control framework for a periodic event-triggered system which is subject to external disturbance and sensor noise. When the disturbance dynamic model is available, and in order to efficiently estimate the state variable and disturbance from non-uniform slow-rate measurements, a time-varying Kalman filter is designed. When the disturbance dynamic model is not available, a disturbance observer is proposed as an alternative approach. Both the Kalman filter and the disturbance observer are proposed in a non-uniform multi-rate format. Such disturbance estimation enables faster controller updating in spite of slower measurement. Interlacing techniques are used in the control system to uniformly distribute the computational load at each fast sampling instance. Compared to the conventional time-triggered sampling paradigm, the control solution is able to reduce the resource utilization, while maintaining a satisfactory control performance. The proposed control solution will reduce the number of transmissions among devices, which enhances the energy and computational efficiency. Simulation results are provided to validate the effectiveness and benefits of the proposed control algorithms.

Periodic event-triggered control of nonlinear systems using overapproximation techniques

In event-triggered control, the control task consisting of sampling the plant’s output and updating the control input is executed whenever a certain event function exceeds a given threshold. The event function typically needs to be monitored continuously, which is difficult to realize in digital implementations. This has led to the development of periodic event-triggered control (PETC), in which the event function is only evaluated periodically. In this paper, we consider general nonlinear continuous event-triggered control (CETC) systems, and present a method to transform the CETC system into a PETC system. In particular, we provide an explicit sampling period at which the event function is evaluated and we present a constructive procedure to redesign the triggering condition. The latter is obtained by upper-bounding the evolution of the event function of the CETC system between two successive sampling instants by a linear time-invariant system and then by using convex overapproximation techniques. Using this approach, we are able to preserve the control performance guarantees (e.g., asymptotic stability with a certain decay rate) of the original CETC system.

H∞ Consensus for Linear Heterogeneous Multiagent Systems Based on Event-Triggered Output Feedback Control Scheme.

In this paper, the H∞ consensus problem for linear heterogeneous multiagent systems (LHMAS) based on event-triggered output feedback control is investigated. Two novel event-triggered control schemes including nonperiodic and periodic event-triggered control approaches are provided to make the LHMAS with external unknown disturbance achieve H∞ consensus. Therein, the nonperiodic event-triggered control method is designed by combining the event-triggered approach with time-triggered scheme, which can make the sampled instants be decided by the event-triggered condition and provide a fixed lower bound of sampled interval to avoid the Zeno-behavior. Then, based on this approach, the periodic event-triggered control scheme has a further improvement that only the information at fixed periodic interval is used for the event-triggered condition, which means that this method avoids the continuous-time information transfer. Besides, both schemes take output feedback control, which means that only the output information of each agent and leader is needed in this paper. Finally, a numerical example is given to support our results.

Asynchronous periodic event-triggered control with dynamical controllers

In this work, we study a networked control system under a periodic event-triggered control strategy. In addition, the input and the output of the system are sampled with different rates, which enables to obtain a compromise between performance and waste of communication resources. Stability analysis and L2-gain analysis are carried out through Lyapunov–Krasovskii techniques. Simulation results of a quadruple-tank process show the benefits of the approach.

Dual-stage periodic event-triggered output-feedback control for linear systems

This paper proposes an event-triggered control framework, called dual-stage periodic event-triggered control (DSPETC), which unifies periodic event-triggered control (PETC) and switching event-triggered control (SETC). Specifically, two period parameters h1 and h2 are introduced to characterize the new event-triggering rule, where h1 denotes the sampling period, while h2 denotes the monitoring period. By choosing some specified values of h2, the proposed control scheme can reduce to PETC or SETC scheme. In the DSPETC framework, the controlled system is represented as a switched system model and its stability is analyzed via a switching-time-dependent Lyapunov functional. Both the cases with/without network-induced delays are investigated. Simulation and experimental results show that the DSPETC scheme is superior to the PETC scheme and the SETC scheme.

Self-Triggered Output Feedback Control for Perturbed Linear Systems

Abstract In this work we propose a Self-Triggered Control (STC) strategy for linear time-invariant (LTI) systems subject to bounded disturbances, using LTI discrete-time dynamic output-feedback. The STC logic computes worst-case triggering times from available information, based on a Periodic Event Triggered Control (PETC) triggering function. In the case of no perturbation and full state information, the discrete times can be determined exactly, defining unions of cones in the state space. When bounded disturbances are present, we compute worst-case triggering times and their associated state-space regions. If full state information is also not available, we use a special observer to compute the worst-case triggering times, yielding an STC logic that only needs the current system output and the controller state. For all cases, we provide sufficient conditions for stability and L2-gain from disturbance to output.