An observation algorithm for nonlinear systems with unknown inputs

Abstract

This paper provides some new developments in the design of unknown input observers for nonlinear systems. An algorithm which states if the state and the unknown input of the system can be recovered in finite time is introduced. This algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers. The proposed method is useful to relax some restrictive conditions of existing nonlinear unknown input observer design procedures.

Causal observability of nonlinear time-delay systems with unknown inputs

“…The result of this section can be seen as an extension of the work [1] to treat the observation problem for time-delay systems with unknown inputs of the form (6). The objective is to generate additional variables from the available measurement and unaffected by the unknown input such that an extended canonical form similar to (11)- (12) can be obtained for the estimation of the remaining state ξ.…”

“…In [1], a constructive algorithm to solve the above mentioned problem for nonlinear systems without delays has been studied. The result of this section can be seen as an extension of the work [1] to treat the observation problem for time-delay systems with unknown inputs of the form (6).…”

A new algorithm to compute inverse dynamic of a class of nonlinear systems

“…This section is based on the algorithm proposed in [19], but in the context of dynamical inversion instead of left inversion [20,10]. Considering again the system (1)-(2) but with singular matrix Γ (for the sake of algorithm's notation denoted Γ 0 ).…”

On Observation of Time-Delay Systems With Unknown Inputs

“…For the case where rank K(δ] Φ < n, although Theorem 2 is not valid, it is still possible to estimate the state and the unknown inputs of (6) provided that some complementary conditions are satisfied. In Barbot et al (2009), a constructive algorithm to solve this problem for nonlinear systems without delays has been proposed, which in fact can be generalized to treat the same problem for nonlinear time-delay systems.…”