Event‐triggered distributed optimisation for multi‐agent systems with transmission delay

Event‐triggered robust output regulation for nonlinear systems: A time regularization approach

“…Proof. From Theorem 1, there exist an output feedback controller (18) and an event-triggered mechanism (8) with (24) such that the state x c of the closed-loop system (19) with x c (0) ∈ Ω n c r approaches zero asymptotically. Then x c is bounded for any x c (0) ∈ Ω n c r and any t ≥ 0.…”

“…It may not be tricky to extend results in this article to the case with the existence of transmission delay especially based on some existing methods. 24,25 It is noted that the component of the event generator is more complex by incorporating an internal model, since in this article, we aim to solve output regulation problem by an output-based control law. It is observed that the structure of the control loop in Figure 1 is also applicable for that in References 4 and 6 although the two essential components, that is, the control input generator and the event generator, work in different ways.…”

“…Suppose that Assumptions 1-5 are satisfied. Given any prescribed compact set S and any x c (0) ∈ Ω n c r with some r > 0, there exist some sufficiently smooth function 𝜌(⋅), some 𝜏, 𝜇 > 0, such that the ETRORP for the nonlinear system ( 1) is solved by a control law (3) with ( 5) and ( 22) and an event-triggered mechanism (8) with (24). Moreover, the ETGRORP for the nonlinear system ( 1) is solved if r = +∞.…”

“…If the transmission delay is considered, the control signal will become $$$ u(t)={\kappa}_1\left(e\left({t}_k\right),\eta \left({t}_k\right),t\right),\kern0.3em t\in \left[{t}_k+{d}_k,{t}_{k+1}+{d}_{k+1}\right) $$$ where $$$ {d}_k $$$ is the delay. It may not be tricky to extend results in this article to the case with the existence of transmission delay especially based on some existing methods 24,25 . It is noted that the component of the event generator is more complex by incorporating an internal model, since in this article, we aim to solve output regulation problem by an output‐based control law.…”

Dynamic event‐triggered cooperative formation control for UAVs subject to time‐varying disturbances

“…In general, two kinds of methods are used to investigate cooperative control of multi‐agent systems, i.e. leader–follower control and leaderless control [1–12]. For the leader–follower approach, the followers track the trajectory of the leader or multiple leaders to achieve the consensus/formation.…”