Robust adaptive £∞-gain neural filtering for non-linear systems in the presence of bounded disturbances

This study deals with the problem of robust adaptive L_∞-gain neural filter design for a class of uncertain systems with unknown non-linearities and persistently bounded disturbances. A neural filter is constructed for the signal estimation of the system, where two radial basis function neural networks (NNs) are employed to approximate the estimates of the unknown non-linearities in the state dynamics and measurement equation of the system, respectively. The addressed problem is to design such a filter such that the state estimation error is uniformly ultimately bounded and the signal estimation error satisfies an L_∞-gain performance. The linear matrix inequality (LMI)-based condition for the existence of a robust adaptive L_∞-gain neural filter is provided. In the proposed filtering scheme, by using the orthogonal projection of the state estimation error onto the null space of the linear measurement distribution matrix, the weight update laws of NNs are represented in terms of the available measurement residual. Furthermore, using the existing LMI optimisation technique, a suboptimal neural filter can be obtained in the sense of minimising an upper bound of the L_∞-gains. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method.