Fixed-time Adaptive Observer for Linear Time-Invariant Systems

Adaptive observers have been applied successfully in many control areas, including adaptive control and fault detection problems. Recently it has been shown that finite-time parameter estimation can improve the overall performance of adaptive controls. If the controller is based on an adaptive observer, then it is natural to assume that the same improvement can be achieved if the adaptive observer converges in finite-time. This problem is addressed in this work for SISO LTI systems. The proposed adaptive observer not only converges in finite-time to the states and parameters, but it also provides a bound of the convergence time which is independent of the initial error. In this sense, it is said that the observer converges in fixed-time.