Robust deterministic least-squares filtering for uncertain time-varying nonlinear systems with unknown inputs

Abstract

The augmented state robust regularized least-squares filter (ASRRLSF) and two-stage robust regularized least-squares filter (TSRRLSF) are proposed for discrete time-varying nonlinear systems with unknown inputs and norm-bounded uncertainties. Unknown inputs affect both state-space model and measurements equation of the system. Combining system states and unknown inputs as an augmented state, the ASRRLSF is developed by converting a deterministic min–max optimization problem to a robust regularized least-squares problem. If dimension of the augmented state increases, the performance of the proposed ASRRLSF will reduce and the computational cost will increase rapidly. Therefore, in the following, the TSRRLSF is proposed by decoupling the ASRRLSF to lower order filters as system states filter and unknown inputs filter using T transformation. Finally, two numerical examples are given in order to illustrate the performance of the proposed filtering approaches.