Observation and Estimation in Linear Descriptor Systems With Application to Constrained Dynamical Systems

Abstract

This paper considers the problems of simultaneous observation or estimation of the positions, velocities, and contact forces in a constrained dynamical system. The equations of such systems are not ordinary differential equations, but descriptor equations, i.e., differential equations where the coefficient of the highest order derivative is singular. An asymptotic observer in descriptor form based on pole assignment techniques is used in the time-invariant case to reconstruct the positions, velocities, and contact forces. For time invariant constrained dynamical systems subject to random disturbances, an optimal estimator in descriptor form is designed based on Wiener-Hopf theory. Constrained dynamical systems yield descriptor systems that are uncontrollable and unobservable at infinity. As a consequence, the observer and estimator may not change the infinite eigenstructure of the system. Examples are given to illustrate the use of our method.