Optimal Robust Filter of Uncertain Fractional Order Systems: A Penalized Deterministic Approach

Developing accurate and optimum state estimation methods for fractional order systems is highly relevant since it provides vital information related to memory effects. The optimum estimation of these systems can be guaranteed using the Kalman filter (KF) when all parameter matrices are not subject to uncertainties. Nevertheless, this fundamental principle of the filter is violated, and its performance can be degraded when the model is uncertain. In this light and to limit this deterioration, the present study introduces an optimal solution for filtering uncertain fractional order systems, which operates as follows. First, using the robust regularized least-squares (RLSs) problem combined with penalty functions, a robust penalty game approach is proposed. Then, in an independent framework of any auxiliary parameters, unified recursive Riccati equation and optimal robust filter are derived subject to norm-bounded uncertainties of parameter matrices. To accomplish this step, the stability and convergence analysis of the filter are illustrated based on the singular theory conception.