An Iterative Learning Scheme-Based Fault Estimator Design for Nonlinear Systems with Randomly Occurring Parameter Uncertainties

This paper deals with fault estimation problem for a class of nonlinear system with parameter uncertainties subjecting to Bernoulli-distributed white sequences with known conditional probabilities. In order to reflect the reality more closely, parameter uncertainties are considered in both the state parameter matrix and the output parameter matrix. Compared with existing observer-based fault estimation approaches, the proposed iterative learning observer considers the state error information and fault estimating information from the previous iteration to improve the fault estimation performance in the current iteration. Simultaneously, the stability and convergence of the designed observer are achieved by employing the Lyapunov stability theory. On the other hand, a novel optimal function using expectation is presented to ensure the uniform convergence of the fault estimation scheme, thus reducing the impact of randomly occurring parameter uncertainties. Finally, linear matrix inequality (LMI) is employed to obtain the solutions of sufficient condition for further improvement of iterative learning law performance. The results are suitable for the systems with time-varying uncertainties as well as constant uncertainties. Additionally, a numerical example is given to demonstrate the effectiveness of the proposed design scheme.