Adaptive Control of Nonlinear Systems with Sinusoidal Uncertainties via Internal Model Principle

In this paper, an adaptive control scheme is established for nonlinear systems with sinusoidal uncertainties from the perspective of internal model principle. We propose to embed the controller with a dynamic compensator which plays the role of an internal model for reproducing the unknown sinusoidal parameter. For linearly parameterized systems, under some full-information stabilizability assumptions, internal-model-based controllers are developed, rendering the closed-loop system trajectories to be bounded and the plant states to be asymptotically convergent to zero. Further, we extend the proposed internal-model-based control scheme to nonlinearly parameterized systems with a (strictly) monotonic assumption. Two simulation examples are given to verify the effectiveness of the proposed schemes.