An ISS-Based Design of Global Robust Adaptive Output Regulators for Nonlinear Systems

Achieving global input-to-state stability (ISS) in closed-loop systems becomes a challenging task when integrating an adaptive scheme into control design. This challenge is particularly prominent in the global output regulation of nonlinear systems. The current state of the art in global robust adaptive output regulators is limited to achieving a weaker form of integral-ISS. In this article, we present an ISS-based design framework for a class of nonlinear systems with input perturbation via a novel adaptive output regulator. Specifically, we introduce a new adaptive internal model comprising an internal model candidate, a parameter estimator, and a filter. This innovative design transforms the original output regulation problem into a robust stabilization problem. We leverage the cyclic small-gain theorem to design a robust stabilizer, ensuring that the resulting closed-loop system achieves global ISS with the perturbation acting as the input.