SYNTHESIS OF INFINITE-DIMENSIONAL OBSERVERS FOR INFINITE-DIMENSIONAL VIBRATING SYSTEMS

The paper is concerned with the synthesis of dynamic observers for infinite-dimensional systems. Specifically, we study infinite-dimensional Luenberger-like observers for infinite-dimensional vibrating systems in a framework of abstract regular systems with only boundary measurement. Exponential convergence of the Luenberger-like observers is proved by using the Lyapunov direct method. Moreover, an estimate of the observer convergence rate is given in terms of the system parameters, which is a desirable property for eventually practical applications. Furthermore, the observer convergence rate is improved by proposing a constructive spectrum assignment algorithm. As an example, explicit Luenberger observers are worked out for an Euler--Bernoulli elastic beam system. Exponential convergence of the designed observers is established by proving regularity and exact observability. Numerical simulations are carried out by the finite element method with the analysis of spectral distribution to evaluate the performance of our designed observers.