Global Output Regulation for Uncertain Feedforward Nonlinear Systems With Unknown Nonlinear Growth Rate

This paper proposes a method for designing an output regulation controller for a class of feedforward nonlinear systems, where the nonlinear terms exhibit an unknown input-dependent rate. The completely unknown nature of this rate introduces significant challenges to control design, rendering existing adaptive and time-varying methods ineffective. To address these challenges, we first introduce a bound on the input and transform the nonlinear condition into an equivalent case with an unknown constant rate. Subsequently, we develop both time-varying and adaptive methods to design the controller. Through rigorous mathematical analysis, we prove that the regulation objective can be achieved under the proposed control framework. Illustrative examples are provided to demonstrate the effectiveness of the designed control strategy.