On Joint Unknown Input and Sliding Mode Estimation

We address state estimation in the presence of faults and unknown disturbances combining unknown input observers (UIOs) and sliding mode observers. We consider a well-established UIO design for linear time-invariant systems and augment it with a nonlinear sliding mode action. This latter term deals with matched disturbances affecting the actuation channels, such as actuator faults, while the UIO provides geometric decoupling from the remaining exogenous inputs. We thoroughly present the analysis of the proposed observer, together with existence conditions stemming from the joint design. We also investigate how our design geometrically relates with other known results in the field of unknown-input state estimation, and discuss its benefits and pitfalls. An advantage of our design is that it allows reconstruction of the fault in finite time, under just boundedness assumptions, while other disturbances are rejected by the UIO. Numerical simulations show the effectiveness of the proposed method.