An accurate estimation of system parameters is crucial for ensuring high-performance modelling and adaptive control of nonlinear systems, particularly in quantized environments. However, existing multi-innovation estimation algorithms often struggle from limited accuracy and slow convergence rate due to the use of batch noise and initial value problem. To address these challenges, this study proposes a multi-innovation repetitive learning-based fractional-order optimization algorithm for extended Wiener systems with backlash nonlinearity under binary-valued data. First, a quantized regression model is established using the parameterization technique of the nonlinear backlash submodel to reduce computational complexity. Drawing on the principle of repetitive learning, a scalar innovation framework with iterative updates is then proposed to mitigate the effect of batch-induced noise. Subsequently, a continuous optimization mechanism is introduced to improve the selection of initial values for parameter estimation. Furthermore, guided by fractional-order theory, a composite correction term is incorporated into the parameter adaptation law to enhance the utilization of quantized system data. Comparative statistical results demonstrate that the proposed estimator achieves superior optimization performance compared with other multi-innovation estimation algorithms in both simulation and real-world applications, thereby highlighting its effectiveness and practical utility.
Gong et al. (Thu,) studied this question.