Dynamic event‐triggered control for a class of p‐normal nonlinear time‐delay systems via output feedback

Abstract

In this article, the event‐triggered (ET) output feedback control problem is discussed for a class of p$$ p $$‐normal nonlinear time‐delay systems. Different from the related existing literature, the linear growth condition is relaxed to the homogeneous one and the growth rate is unknown. In the case of unknown time‐varying delays and control coefficients, nonsmooth control law and some extra redundant terms will be encountered in the design of ET controller, which would bring substantial challenges to the achievement of global convergence. To cope with unknown growth rate and time‐varying delays, two dynamic gains and an appropriate Lyapunov–Krasovskii functional (LKF) are introduced. Then, a new dynamic ET mechanism is given, in which the triggering threshold can be tuned dynamically. It is proved that all the signals of the closed‐loop system (CLS) are bounded. Corresponding examples are given to indicate the validity of the developed theoretical results.

Reduced‐order observer‐based adaptive event‐triggered output feedback tracking control for a class of nonlinear systems with more general nonlinearities

“…An adaptive event‐triggered output feedback stabilizing controller was proposed in Reference 18 for a class of $$$ p $$$‐normal nonlinear systems with sensor multiplicative error, where a dynamic gain and a series of constant gains were designed to ensure the asymptotic stability. Similar research can be seen in Reference 19, in which time‐varying delays in system nonlinearities were considered and two dynamic gains were constructed. In Reference 20, by introducing a dynamic gain to compensate for system nonlinearities and execution error, an adaptive event‐triggered output feedback stabilization was proposed for a class of uncertain nonlinear systems, in which the system nonlinearities depend on unmeasurable states and satisfy linear growth condition.…”

“…First of all, for the event-triggered mechanism, from (19), it implies that for any interval [t j , t j+1 ), j ∈ {0, 1, 2, … },…”

“…in which, together with the boundedness of l, implies that there exists a positive constant D 1 such that l ≤ D 1 . Moreover, with the triggering condition (19), since…”

“…All the triggering instants and triggering types are shown in (F). Furthermore, Table 1 shows that the totally triggering numbers are 236, the numbers of event (19) and event (20) are 21 and 215, and the Zeno phenomenon is avoided since the minimum interval of event is 0.0021s.…”

“…Figure 3F shows all the triggering instants and triggering types, where the blue symbol "⊳" denotes that ( 19) is triggered and the red symbol "⊲" denotes that (20) is triggered. As shown in Table 1, the totally triggering numbers are 344, in which the numbers of event (19) are 34 and the number of events (20) are 310. Moreover, the minimum interval of event is 0.0016s, which implies that the Zeno phenomenon is avoided.…”