Adaptive Event-triggered Control with Sampled Transmitted Output and Controller Dynamics

TL;DR

This work addresses reducing communication in networked control of uncertain nonlinear systems by moving all controller components to the controller side and employing sampled-state dynamics with two event detectors to govern transmissions. It develops a state observer, adaptive law, and dynamic filter within a backstepping framework to cope with non-differentiable virtual inputs, and proves semiglobal boundedness of all internal signals along with practical stabilization of the output, while excluding Zeno behavior. A key contribution is a lemma that bounds the error between the actual output $y$ and the sampled transmitted output $\bar{y}$, enabling stability analysis under intermittent communication. Numerical simulations illustrate effective control with fewer transmissions compared to prior work, validating the practicality of controller-side sampling and the proposed adaptive scheme for uncertain nonlinear plants over networks.

Abstract

The event-triggered control with intermittent output can reduce the communication burden between the controller and plant side over the network. It has been exploited for adaptive output feedback control of uncertain nonlinear systems in the literature, however the controller must partially reside at the plant side where the computation capacity is required. In this paper, all controller components are moved to the controller side and their dynamics use sampled states rather than continuous one with the benefit of directly estimating next triggering instance of some conditions and avoiding constantly checking event condition at the controller side. However, these bring two major challenges. First, the virtual input designed in the dynamic filtering technique for the stabilization is no longer differentiable. Second, the plant output is sampled to transmit at plant side and sampled again at controller side to construct the controller, and the two asynchronous samplings make the analysis more involving. This paper solves these two issues by introducing a new state observer to simplify the adaptive law, a set of continuous companion variables for stability analysis and a new lemma quantifying the error bound between actual output signal and sampled transmitted output. It is theoretically guaranteed that all internal signals in the closed-loop system are semiglobally bounded and the output is practically stabilized to the origin. Finally, the numerical simulation illustrates the effectiveness of proposed scheme.

Figures (10)

• Figure 1: Illustration of the proposed output feedback control strategy with output, controller, state observer, adaptive law, dynamic filter, and event detectors. $\otimes$ denotes the combination of different signals; $\bullet$ denotes the replication of signal. ZOH is zero-order holder which can transform discrete signals into piecewise-continuous signals.
• Figure 2: The trajectories of actual output $y(t)$ and triggered output $\bar{y}(t)$.
• Figure 3: The trajectory of actual controller $u(t)$.
• Figure 4: Trigger events of ED1 and ED2.
• Figure 5: The trajectories of state observer $\dot\xi_1(t)$, $\dot\xi_2(t)$, $\dot\zeta_1(t)$, $\dot\zeta_2(t)$.