Periodic Event-Triggered Suboptimal Control With Sampling Period and Performance Analysis.

In this paper, we were concerned with the periodic event-triggered asynchronous stabilization of a class of hybrid stochastic systems driven by continuous-time Markov chain and Brownian motion, where the measurements of state and mode were available only at sampling instants, and the control was diffusion-dependent. Static and dynamic periodic event-triggered control (PETC) strategies were proposed with a guaranteed minimum interevent time for every sample path solution. Different from the well-known input-to-state stability framework for stability and synthesis of event-triggered control systems, a comparison system approach was developed to show that if the hybrid stochastic system under continuous-time feedback control was $ p $th-moment exponentially stable, then there existed a small sampling period and event-triggering parameters such that the resulting event-triggered control hybrid stochastic system was almost surely exponentially stable. Particularly, the proposed PETC strategies could integrate the beneficial impacts of stochastic noises, which distinguished them from previous results. Two numerical examples were provided to illustrate the efficiency of the theoretical results.

In this paper, a novel event-triggered control (ETC) strategy is proposed by striking a balance between periodic sampled-data control and ETC. This leads to so-called periodic event-triggered control (PETC), in which the advantage of reduced resource utilisation is preserved on the one hand, while, on the other hand, the conditions that trigger the events still have a periodic character. The latter aspect has the advantage that the event-triggering condition has to be verified only at the periodic sampling times, instead of continuously, as in conventional ETC. To analyse the stability and the L 2 -gain properties of the resulting PETC systems, two different approaches will be presented based on (i) piecewise linear systems, and (ii) impulsive systems, respectively. Moreover, the advantages and disadvantages of each of the methods will be highlighted. The developed theory will be illustrated using a numerical example.

In this paper, the stability problem for event-triggered nonlinear control systems is addressed in the presence of stochastic denial of service (DoS) attacks on the communication network. Dynamic event-triggered control (DETC) and periodic event-triggered control (PETC) are considered under the stochastic attacks. The stochastic attacks are modeled by a stochastic hybrid timer and a logic variable which is used to identify whether the network is attacked or not. Then the entire closed-loop system can be modeled into the framework of stochastic hybrid systems. Uniform global asymptotic stability in probability is concluded for the resulting stochastic system by proving that the equilibrium set is uniformly globally stable in probability and each neighborhood of the equilibrium set is uniformly globally recurrent. A nonlinear system example is provided to illustrate the effectiveness of the proposed results.

This paper investigates the periodic event-triggered asymmetric bipartite consensus problem of multi-agent systems (MASs) under structurally balanced undirected signed graphs. In order to reduce the consumption of communication resources and continuous detection in the control process of MASs, a novel periodic detection event-triggered asymmetric bipartite consensus control protocol is proposed. In particular, each agent samples only in a fixed period. For each agent, two event conditions are given, and only when state error satisfies this event condition can the event be triggered. A new type of Laplacian matrix is constructed to achieve asymmetric bipartite consensus. The control method can guarantee the performance of MASs and have less communication resources. Based on the Lyapunov stability theorem and algebraic graph theory, the proposed periodic event-triggered control strategy is able to implement the asymmetric bipartite consensus when the topology is structurally balanced undirected signed graphs. The proposed method in this paper can reduce the restriction on the sampling period and automatically exclude Zeno behavior. Finally, the validity of the conclusion is verified by numerical simulation.

Periodic event-triggered state-feedback control for discrete-time linear systems

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

In this work we are interested in the stability and ℒ2-gain of hybrid systems with linear flow dynamics, periodic time-triggered jumps and nonlinear possibly set-valued jump maps. This class of hybrid systems includes various interesting applications such as periodic event-triggered control. In this paper we also show that sampled-data systems with arbitrarily switching controllers can be captured in this framework by requiring the jump map to be set-valued. We provide novel conditions for the internal stability and ℒ2-gain analysis of these systems adopting a lifting-based approach. In particular, we establish that the internal stability and contractivity in terms of an ℒ2-gain smaller than 1 are equivalent to the internal stability and contractivity of a particular discrete-time set-valued nonlinear system. Despite earlier works in this direction, these novel characterisations are the first necessary and sufficient conditions for the stability and the contractivity of this class of hybrid systems. The results are illustrated through multiple new examples.

This paper develops a new estimate-based dynamic event-triggered output feedback controller for networked control systems subject to nonlinear uncertainties. Specifically, based on the sampled-data, a discrete-time output feedback controller and a discrete-time dynamic event-triggering condition are proposed by the virtue of feedback domination technique. The proposed event-triggered control method is easy to implement in digital computers due to the form of discrete time. Under the proposed dynamic event-triggered control method, the selection regions of the sampling period and the scaling gain are explicitly given to guarantee the global practical/asymptotic stability of the closed-loop system. Finally, two examples are employed to verify the efficiency of the proposed dynamic event-triggered control approach.

Event-triggered networked control of a linear dynamical system is investigated. Specifically, the dynamical system and the controller are assumed to be connected through a communication channel. State and control input information packets between the system and the controller are attempted to be exchanged over the network only at time instants when certain triggering conditions are satisfied. We provide a probabilistic characterization for the link failures which allows us to model random packet losses due to unreliability in transmissions as well as those caused by malicious jamming attacks. We obtain conditions for the almost sure stability of the closed-loop system, and we illustrate the efficacy of our approach with a numerical example.

Event-triggered control for input constrained non-affine nonlinear systems based on neuro-dynamic programming

In the existing memory event-triggered control (METC) algorithms, the threshold parameters and memory weights are fixed, reducing the system’s adaptability. In this paper, a new intelligent dynamic METC algorithm is proposed to reduce the amount of transmission data and decrease the communication burden in networked control systems. The proposed dynamic METC mechanism applies the gradient-sharing asynchronous advantage actor-critic (A3C-GS) learning algorithm to optimized memory event-triggered function of memory weights and threshold parameters. A time-varying delay system model for dynamic METC is developed by incorporating the A3C-GS for the networked control system with communication delays. Then, by solving two linear matrix inequalities (LMIs), the controller gain parameters of the networked control systems are derived. Finally, the performance of the proposed new METC algorithm is compared with the current three event-triggered control methods. Simulation results show that the proposed intelligent event-triggered algorithm reduces the number of triggers by about 40% compared with the traditional event-triggered algorithm under the pregiven simulation time. Thus, the effectiveness of the main results is verified.

This paper proposes an event-triggered model predictive control (ET-MPC) method for the three-phase inverter with output LC filter. The proposed method is developed by combining the conventional finite-control-set MPC (FCS-MPC) method and the ET control strategy. The ET control strategy incorporates a preset triggering condition based on the requirement of the regulation performance for the three-phase inverter. When the state of the three-phase inverter activates the triggering condition, FCS-MPC is triggered with the updated state so that the optimal control actions can be generated when it is necessary. If the state of the inverter is within the preset triggering condition, FCS-MPC is suspended and the control actions are held as constant. Consequently, the unnecessary online prediction, online optimization, and the corresponding control actions can be avoided. Therefore, with the tolerate regulation performance, the proposed ET-MPC can reduce the computational burden of the conventional FCS-MPC. The various simulation studies of the three-phase inverter are conducted and discussed to demonstrate the effectiveness of the proposed ET-MPC method.

This note considers the active secure event-triggered control(ETC) problem of hybrid power system under DoS attack. A combination of load frequency control (LFC) and virtual inertia control (VIC) is adopted to deal with the influence of uncertainty and lower inertia induced by renewable energy like wind and solar power. To active defend DoS attack interrupting communication of measurement and control, an interval secure event-triggered mechanism (ISETM) is proposed under software defined network (SDN). Both a triggering transmission and a secure triggering interval are generated where the triggering packet is transmitted over SDN data plane and the secure triggering interval is sent to SDN control plane regulating SDN cybersecurity mechanism. Under ISETM, multi-area hybrid power system is modeled by a delay system with two triggering conditions. Furthermore, interval secure event-triggered LFC-VIC of hybrid power system is formulated by a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $ </tex-math></inline-formula> control problem. A sufficient criterion of hybrid power system with the prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $ </tex-math></inline-formula> performance level is derived by using Lyapunov-Krasovskii functional method. A co-designed method of ISETM and LFC-VIC gains is given by linear matrix inequalities (LMIs). Finally, a two-area hybrid power system is simulated to verify the validness of the proposed interval secure event-triggered control (ISETC) method.

Resources limitations of embedded systems and networked control systems have motivated the development of novel controller implementation paradigms in order to reduce the potential conservatism of traditional clock-driven setups. In this context periodic event-triggered control has recently been proposed. Based on a periodically evaluated and state-dependent criterion, it is decided, at every sampling instant, whether the control input needs to be updated or not. In this paper we propose a method for the design of periodic event-triggered controllers for nonlinear systems. We follow an emulation-based approach as we start from a known (continuously evaluated) event-triggered controller and we provide a systematic technique to select the sampling period and to redesign the triggering condition to approximately maintain the guarantees ensured by the original controller. The method is illustrated on a physical system and we compare the obtained results with other available event-based implementations.

This paper addresses periodic event-triggered output-feedback control (PETOFC) and event-triggered state-feedback control (ETSFC) for polynomial systems modeled by a linear-like representation with state-dependent coefficients. Periodic event-triggering evaluates conditions at fixed intervals, preventing Zeno behavior, while state-feedback control guarantees a minimum inter-event interval. Stability is analyzed using linear matrix inequalities. Under the proposed event-triggered controllers and using the sum-of-squares programming, the asymptotic stability of the closed-loop systems is ensured. Finally, the effectiveness of the proposed controllers are illustrated through two numerical examples.