Consensus of multiagent systems with time‐varying delays: An observer‐based distributed periodic event‐triggered control approach

Abstract

This work presents a consensus strategy for multiagent networked systems with time‐varying delays. A new control technique is first developed, named observer‐based distributed periodic event‐triggered control. Aiming at leader‐following consensus strategy, the state update of every follower agent just demands the neighbor state at the moment of its own event. Then, based on matrix inequalities, the sufficient criteria for the systems under consideration are established, which is easier to satisfy and shows that the consensus can be reached exponentially. Finally, one numerical example is presented to indicate the performance of the proposed method.

Adaptive critic learning for event‐triggered safe control of nonlinear safety‐critical systems

“…According to the Weierstrass approximation theorem [30][31][32], in the safe set , the optimal safe cost function V * (x) is constructed as follows:…”

“…However, for the updating law (31), according to earlier studies [35,39], we know that in order to approximate W c with Ŵc , the PE condition must be satisfied. However, satisfying the PE condition usually requires the addition of an exploration noise signal, which might lead to the system being into the unsafe set or even instability [36,37].…”

“…According to the Weierstrass approximation theorem [30–32], in the safe set $$$ \mathcal{C} $$$, the optimal safe cost function $$$ {V}^{\ast }(x) $$$ is constructed as follows: $$$$ {V}^{\ast }(x)={W}_c^T\phi (x)+\varepsilon (x), $$$$ where $$$ {W}_c\in {\mathbb{R}}^n $$$ is the ideal weight, $$$ \phi (x)\in {\mathbb{R}}^n $$$ and $$$ \varepsilon (x)\in \mathbb{R} $$$ denote the suitable activation function and the approximation error of NN, respectively, and $$$ n $$$ is the number of hidden neurons. The derivative of optimal safe cost function $$$ {V}^{\ast }(x) $$$ with respect to $$$ x $$$ is as follows: $$$$ \nabla {V}^{\ast }(x)=\nabla {\phi}^T(x){W}_c+\nabla \varepsilon (x).$$…”

“…Compared with the TTC, the ETC reduces a lot of extra uncalled-for calculations and communications [28][29][30]. Therefore, the event-triggered mechanism has been rapidly developed and widely used [31,32]. In Vamvoudakis [30], Vamvoudakis proposed an optimal adaptive control algorithm under event-triggered framework by using actor-critic neural networks for nonlinear continuous-time systems.…”

Adaptive event‐triggered control of multi‐agent systems with state constraints and unknown disturbances

“…In ref. [52], a consensus strategy for multiagent networked systems with time varying delays is studied by aiming at leader-following consensus strategy. The methods mentioned above have a common feature that they do not take into account the impact of constraints on event-triggered control.…”