Input Observer For Linear Systems Research Articles

Adaptive distributed unknown input observer for linear systems

This paper studies the adaptive distributed unknown input observer (ADUIO) for linear systems with local outputs, which contains a group of local observers under directed graph. The difficulty is the adaptive estimation of global output for the systems with unknown inputs. To solve the problem, disturbance decoupling principle and leader-following consensus strategy are integrated to estimate local outputs of other observers, which can be accumulated to recover the global outputs. Based on the estimated global outputs, an ADUIO is constructed to estimate the full state which avoids using local output matrices of other observers and global information of the graph. Different from the extensive joint detectability assumption in existing results, a detectability assumption is given to make the estimation errors converge to zero asymptotically.

Minimal-order specified-time unknown input observers

This paper presents a framework on minimal-order specified-time unknown input observers for linear systems based on a pairwise observer structure. A minimal-order specified-time observer is first proposed for the linear system without the unknown input, which can estimate the state exactly at the preset time by seeking for the unique solution of a system of linear equations. To further release the computational burden, another form of the specified-time observer is designed. In the presence of the unknown input, it is shown that the existing reduced-order specified-time unknown input observer is not the minimal-order one. By introducing a singular transformation to decouple the effect of the unknown input, the minimal-order specified-time unknown input observer is presented, with the strong* observability capturing the sufficient and necessary condition. The robustness of the proposed observers is also discussed.

Residual generation with unknown input observer for linear systems in the presence of unmatched uncertainties

In this paper, we deal with residual vector generation for fault detection problems in linear systems via unknown input observer (UIO) when the so-called observer matching condition is not satisfied. Based on the relative degree between unknown input and output, a vector of the auxiliary output is introduced so that the observer matching condition is satisfied with respect to the vector. Auxiliary outputs are related to the derivatives of measured signals. However, differentiation leads to excessive amplification of measurement noise. A dynamically equivalent configuration of linear systems is developed using successive integrations to avoid differentiation. As such, auxiliary outputs are constructed without differentiation. Then, the equivalent dynamic system and its corresponding auxiliary outputs are used to generate the residual vector via an exponentially converging UIO. Fault detection in the generated residual vector is also investigated. Finally, the effectiveness of the proposed method is shown via numerical simulation.

Design of unknown input observers for linear systems with unmatched unknown inputs

We discuss an algebraic design of unknown input observers (UIOs) for linear systems with unknown inputs that do not satisfy the observer matching condition. Such a condition is often required for the existence of a UIO. To circumvent the restriction imposed by the observer matching condition, auxiliary outputs defined as the higher-order derivatives of the output measurements are introduced so that the observer matching condition is satisfied with respect to unknown inputs. The augmented outputs consisting of both the output measurements and the auxiliary outputs are defined, where the auxiliary outputs are estimated using higher-order sliding-mode exact differentiators based on the output measurements. Through suitable coordinate transformations, a system with the augmented outputs can be partitioned into two interconnected subsystems: an unknown input-free subsystem and an unknown input-dependent subsystem. The state vectors of the second subsystem are described in terms of augmented outputs. The unknown input-free subsystem is then used to design a UIO for estimation of the state vector. The performance of the UIO is verified through simulated numerical examples.

Unknown input observer for state affine systems: A necessary and sufficient condition

The problem of designing an unknown input observer for linear systems and its application to fault detection is widely studied in the literature. For nonlinear systems, only subclasses of nonlinear systems and sufficient conditions have been stated. In this paper an unknown input observer design for state affine systems is considered. Based on the geometric approach, a necessary and sufficient condition is given for the existence of an unknown input observer.