Adaptive control with nonlinear reference systems

Although reference systems with linear dynamics are common in the adaptive control literature, they can lead to limitations on the achievable closed-loop dynamical system performance. This is due to the fact that linear reference systems can only approximate the desired closed-loop behavior of nonlinear dynamical systems in narrow regions of the state-space. In this paper, we study a new adaptive control architecture for uncertain dynamical systems based on a nonlinear reference system. It is shown that the system error between the uncertain dynamical system and the nonlinear reference system asymptotically vanishes in steady-state, and its performance is guaranteed during the transient-time. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed methodology.