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

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 the system uncertainties and nonlinearities. The key idea of the proposed approach is that whenever the Lyapunov function does not decrease as desired, the switching mechanism is activated so that a new gain is adopted. 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, which is of concise form and low complexity, is proposed based on the developed switching mechanism. It is shown that the objective of global regulation is achieved with faster convergence speed and better transient performance under the proposed controller. Moreover, it is also shown that the proposed control approach can be extended with the enhanced switching mechanism to deal with feedforward nonlinear systems with external disturbances. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of our approach in comparison with the existing approaches.