Global Regulation of Feedforward Nonlinear Systems: A Logic-Based Switching Gain Approach

TL;DR

This paper tackles the global regulation problem for feedforward nonlinear systems with unknown input-output-dependent growth rates, formulates a generalized growth-bound model with $p\in[0,1/n)$, and introduces a novel logic-based switching (LBS) gain alongside a tanh-type speed-regulation function to enhance convergence. The core method combines a low-gain observer with a switching state-feedback structure (SAOF) and a carefully designed switching mechanism to achieve bounded signals and asymptotic state convergence. The key contributions include (i) a general growth-rate model accommodating unknown constants and disturbances, (ii) a low-complexity SAOF controller with an LBS gain and a tanh speed regulator, and (iii) disturbance-tolerant extensions with finite switching and guaranteed convergence. Practically, the approach yields faster convergence, improved transient performance, and robustness to unknown disturbances, demonstrated via representative simulations and comparisons against existing gain-scaling methods.

Abstract

In this article, we investigate the global regulation problem for a class of feedforward nonlinear systems. Notably, the systems under consideration allow unknown input-output-dependent nonlinear growth rates, which has not been considered in existing works. A novel logic-based switching (LBS) gain approach is proposed to counteract system uncertainties and nonlinearities. Furthermore, a tanh-type speed-regulation function is embedded into the switching mechanism for the first time to improve the convergence speed and transient performance. Then, a switching adaptive output feedback (SAOF) controller is proposed based on the developed switching mechanism, which is of a concise form and low-complexity characteristic. It is shown that the objective of global regulation is achieved with faster convergence speed and better transient performance under the proposed controller. Moreover, by strengthening the switching mechanism, the improved control approach can deal with feedforward nonlinear systems with external disturbances. Finally, representative examples are presented to demonstrate the effectiveness and advantages of our approach in comparison with the existing approaches.

Figures (2)

• Figure 1: The trajectories of speed-regulating function $\varphi (t,\mu )$ under different adjustable constants.
• Figure 2: The trajectories of $x_{i}$ and $x_{i}-\hat{x}_{i}$, $i=1,2,3$, in Example \ref{['example1']}.

Theorems & Definitions (11)

• Lemma 1
• Remark 1
• Remark 2
• Theorem 1
• Remark 3
• Theorem 2
• Remark 4
• Remark 5
• Remark 6
• Example 1