Adaptive control for uncertain dynamical systems with nonlinear reference systems

A reference model of an adaptive control law defines how a closed-loop dynamical system under consideration has to asymptotically (or approximately) behave in the presence of system uncertainties. While it is of common practice to use reference models with linear dynamics, this can lead to limitations on the achievable closed-loop dynamical system performance – especially for applications involving highly capable dynamical systems such as highly manoeuvrable aircraft, missiles, and space launch vehicles. Because, linear reference models for these applications can only approximate the desired closed-loop behaviour of these nonlinear dynamical systems in narrow regions of the state-space. Motivated from this standpoint, this paper's contribution is to present a new adaptive control architecture for uncertain dynamical systems based on nonlinear reference models. Specifically, we analytically show that the system error between the uncertain dynamical system and the nonlinear reference model asymptotically vanishes in steady-state and its performance is guaranteed during the transient-time. We further discuss the practicality of our approach and provide numerical examples to demonstrate its efficacy.