Periodic event-triggered control of nonlinear systems using overapproximation techniques

Abstract

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 bound on the 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.

Periodic Event-Triggered Control for Nonlinear Networked Control Systems

“…Suppose that Assumption 3 holds with α V (x, e, w) = α W (|e|) − V (|w|) for some α W , V ∈ K ∞ from Assumption 3. Let λ ∈ [0, λ * ) and T < T MASP (λ), where λ * and T MASP (λ) are defined in (17) and (18), respectively. Then, set A defined in Theorem 1 is ISS.…”

“…, where λ * and T MASP (λ) are defined in (17) and 18, respectively. Then, system (9) is L p -stable from w and to z with respect to the set A defined in Theorem 1 with gain less than or equal to θ.…”

“…This is different from PETC as done in the paper, as the triggering conditions here are evaluated only at some sampling instants, which facilitates digital implementations. Compared to [9, Chapter 6.5] and [17], the results are applicable for decentralized output-feedback control, tolerate the presence of exogenous disturbances and explicitly reveal a link between the triggering conditions and the sampling instants. Compared to [18], we consider exogenous disturbances, a decentralized scenario, we do not restrict our attention to nonlinear systems with a specific structure, and we ensure asymptotic stability in the absence of perturbations.…”

“…On the other hand, PETC results for nonlinear systems are scarce. In [9,Chapter 6.5] and [17], it is explained how to convert general continuous state-feedback event-triggered controllers to periodic event-triggered ones, while (approximately) preserving the properties of the former. The work in [18] develops observer-based output-feedback controllers for a class of nonlinear Lipschitz systems and a practical stability property is ensured at the end.…”

Probabilistic‐constrained filtering for a class of nonlinear systems with improved static event‐triggered communication

“…23 Later, the periodic ETS was extended to the nonlinear system using over approximation techniques. 24 When considering the wireless sensor/actuator networks or multiagent systems, the decentralized ETS and distributed ETS were investigated in the works of Mazo and Tabuada, 25 Tian and Yue, 26 and Wang and Hovakimyan. 27 It should be pointed out that most of the aforementioned researches are static ETS, that is, the parameter in triggering conditions is time invariant.…”