Filtering-Based Concurrent Learning Adaptive Control: Exponential Convergence of System Parameters and Control Coefficient

This paper presents a filtering-based concurrent learning (FCL) adaptive control technique for a class of nonlinear systems with parameter uncertainties and unknown control coefficient. The proposed FCL builds on the baseline CL, which was created to achieve exponential convergence of either system parameters or control coefficient while relying on the estimation of state derivatives using numerical methods. To extend CL, the key point is to define an adaptation mechanism that records the filtered basis of the system instead of the original basis while there is no need for numerical methods to estimate the state derivatives. For this purpose, we first suggest the control law that uses the estimates of unknown parameters and state derivatives, and then show how to derive the FCL adaptation law. The main contribution of this paper is that system parameters, control coefficient, and tracking errors are all exponentially convergent which is ensured by using a Lyapunov argument. Simulations on four illustrative examples—an underwater vehicle, an inverted pendulum, the wing rock model, and a Segway—are finally carried out to validate the soundness of the proposed technique.