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Hybrid Event-triggered Control of Nonlinear System with Full State Constraints and Disturbance

Ziming Wang

TL;DR

This work addresses adaptive tracking for a nonlinear time-varying system with full-state constraints and unknown disturbances. It combines a log-based barrier via an auxiliary system, an RBFNN-based disturbance observer, and a first-order differentiator to tame backstepping complexity, all within a Hybrid Event-Triggered Control framework that blends fixed and relative thresholds. The main contributions include transforming constrained dynamics, proving SGUUB stability, and demonstrating substantial reductions in communication events without inducing Zeno behavior, validated through a simulation. The approach enhances robustness to disturbances while efficiently utilizing network resources, making it practical for resource-constrained control systems.

Abstract

This article focuses on the problem of adaptive tracking control for a specific type of nonlinear system that is subject to full-state constraints via a hybrid event-triggered control (HETC) strategy. With the auxiliary system, we proposed a 'log' function to deal with the full-state constraint. Additionally, a disturbance observer (DO) is constructed to handle the unmeasurable external disturbance. Then, by employing radial basis function neural networks (RBFNNs) and a first-order differentiator, an opportune backstepping design procedure is given to avoid the problem of "explosion of complexity". The HETC strategy, including the fixed and relative threshold, is presented to provide more flexibility in balancing the system performances and network burdens. Finally, to demonstrate the effectiveness of the aforementioned control scheme, a simulation example is presented to validate its effectiveness.

Hybrid Event-triggered Control of Nonlinear System with Full State Constraints and Disturbance

TL;DR

This work addresses adaptive tracking for a nonlinear time-varying system with full-state constraints and unknown disturbances. It combines a log-based barrier via an auxiliary system, an RBFNN-based disturbance observer, and a first-order differentiator to tame backstepping complexity, all within a Hybrid Event-Triggered Control framework that blends fixed and relative thresholds. The main contributions include transforming constrained dynamics, proving SGUUB stability, and demonstrating substantial reductions in communication events without inducing Zeno behavior, validated through a simulation. The approach enhances robustness to disturbances while efficiently utilizing network resources, making it practical for resource-constrained control systems.

Abstract

This article focuses on the problem of adaptive tracking control for a specific type of nonlinear system that is subject to full-state constraints via a hybrid event-triggered control (HETC) strategy. With the auxiliary system, we proposed a 'log' function to deal with the full-state constraint. Additionally, a disturbance observer (DO) is constructed to handle the unmeasurable external disturbance. Then, by employing radial basis function neural networks (RBFNNs) and a first-order differentiator, an opportune backstepping design procedure is given to avoid the problem of "explosion of complexity". The HETC strategy, including the fixed and relative threshold, is presented to provide more flexibility in balancing the system performances and network burdens. Finally, to demonstrate the effectiveness of the aforementioned control scheme, a simulation example is presented to validate its effectiveness.
Paper Structure (8 sections, 52 equations, 3 figures)

This paper contains 8 sections, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Full State Constraints
  4. Disturbance Observer
  5. Hybrid event-triggered control
  6. Adaptive Control Design
  7. Validation
  8. Conclusions

Figures (3)

  • Figure 1: Block diagram of the adaptive control framework with HETC.
  • Figure 2: Desired trajectories $m_r$ and outputs $m_1$, the interval of HETC.
  • Figure 3: Control signal $u(t)$, estimated parameter $\varphi$ and phase portrait of two disturbance observer errors.