An output-feedback stabilisation scheme with exponential convergence for nonlinear systems with unknown polynomial-of-output growth rate

This paper seeks adaptive output-feedback control which enables exponential stabilisation for nonlinear systems with unknown polynomial-of-output growth rate and dynamic uncertainties. The existence of uncertainties naturally requires the introduction of adaptive compensation mechanisms, while, convergence rate, as an important performance specification, is usually hard to attain in the context of adaptive control. For this, we are compelled to pursue a comprehensive and competent adaptive compensation mechanism which possesses dual capabilities of compensating uncertainties and affording convergence rate. Crucially, a subtle dynamic gain is designed with its dynamic updating law incorporating exponential-type time-varying information. Notably, the gain would not only deal with the unknown polynomial-of-output growth rate but particularly ensure exponential convergence with the convergence rate online adjusting in conformity to the dynamic uncertainties. Correspondingly, an adaptive output-feedback controller is constructed based on a dynamic-gain observer, which can render exponential convergence for system and observer states.