Differentiation-based State Estimationin LTI Systems with unknown Inputs

Activity: Talk or presentationInvited talkScience to science


In various applications in the field of control engineering the estimation of the state variables of linear time-invariant systems in the presence of unknown inputs plays an important role. Existing methods require the so-called observer matching condition to be satisfied, rely on the boundedness of the state variables or exhibit an increased observer order of twice the plant order.
In this talk, a new differentiation-based approach for the design of a robust observer is presented. Its application is not restricted to systems which satisfy the aforementioned limitations of already existing unknown input observers. This is achieved by proposing a novel observer normal form for strongly observable linear time-invariant multivariable systems. In contrast to classical normal forms, the proposed approach also takes the unknown inputs into account. The proposed observer normal form allows for the straightforward construction of a higher-order sliding mode observer, which ensures global convergence of the estimation error within finite time even in the presence of unknown bounded inputs. In the case of a system with one single unknown input and one single output the observer design reduces to a simple and elegant procedure which can be regarded as a nonlinear generalization of Ackermann’s eigenvalue placement.
The proposed approach can be exploited for the reconstruction of unknown inputs with bounded derivative and robust state-feedback control. Numerical simulations confirm the effectiveness of the presented work.
Period29 Sep 2021
Held atNational Autonomous University of Mexico, Mexico
Degree of RecognitionInternational