An Enhanced Strategy for Adaptive Output-Feedback Control of Uncertain Nonlinear Systems

We are concerned with global practical tracking for uncertain nonlinear systems with intrinsic dependence on unmeasured states. Typically, we aim to remove the polynomial restrictions on system growth rates in relevant works, admitting the rates to be of arbitrary function-of-output type. Note that such highly nonlinear rates could alter so drastically in magnitude that no polynomial can upper bound them on any unbounded region, and would undermine the design rationale and the analysis route that are followed in polynomial rate scenarios. This entails refining/integrating state-of-the-art techniques and developing new ones, from design to analysis. Concretely, to circumvent the need for knowledge on polynomials, dual dynamic high gains are devised ingeniously which particularly incorporate certain highly nonlinear components to counteract the arbitrary function-of-output rates and other inherent nonlinearities and uncertainties. But unfavorable impacts of the components would also arise putting the effectiveness of the high gains at risk, which necessitates noticeable changes in the choice of vital variables/functions. In addition, to provide tractable observer error dynamics for control design and analysis, a nonlinear high-gain observer is pursued, which is filter based and of reduced order, following the design methodologies in relevant works. In terms of performance analysis, practical tracking suffers extra time variants and additive uncertainties which together with the highly nonlinear rates would carry over to stability analysis inevitably and in turn ruin the existing analysis routes. Hence, a new analysis route is paved to verify the anticipated performance. Notably, by unfolding an important implication, the performance verification boils down largely to the boundedness of the high gains. This makes plain and intelligible the verification, although sophisticated integration of multiple composite Lyapunov functions is still required. An exception, i.e., asymptotic stabilization, is presented to demonstrate its close connection with practical tracking.