Observer-based adaptive neural network control: the convergence properties analysis under the influence of persistent excitation level

In this paper, an observer-based adaptive neural network (NN) control method is proposed for a class of nonlinear systems. A crucial component of output feedback control is the state observer, with high gain observers widely used to estimate system states. When the system exhibits unknown dynamics, a higher gain is typically required to eliminate these effects. However, the higher gain amplifies the impact of measurement noise, thereby reducing the performance of the observer. To address this issue, we employ the adaptive high gain observer to reconstruct the system state, utilizing NNs to estimate the unknown dynamics, which allows for the selection of a relatively lower observer gain. It is noted that the convergence of the NN weights must satisfy the persistent excitation (PE) condition, which is often challenging to achieve in practice. By employing the deterministic learning method, the partial PE condition of the radial basis function NN is satisfied. Furthermore, how the PE condition influences observer performance, and subsequently affects controller performance, is explored through convergence analysis in adaptive estimation. Notably, a higher PE level (the lower bound of PE) also helps mitigate the effects of measurement noise. A simulation example is provided to demonstrate the effectiveness of the proposed method.