Adaptive observer design for a class of MIMO nonlinear systems

For a class of uniformly observable nonlinear multi-input-multi-output (MIMO) systems with unknown parameters in both state and output equations, an adaptive observer is designed in a constructive manner based on the techniques of high gain observer and adaptive estimation. The high gain adaptive observer for joint state and unknown parameter estimation is conceptually simple. The new algorithm makes use of a time varying gain matrix for unknown parameter estimation, which simplifies the initialization and parameter tuning. In order to establish the global exponential convergence of the adaptive observer, a persistent excitation condition is required. Consequently, the global exponential convergence for simultaneous estimation of states and unknown parameters is formally established following a simple procedure. A numerical example is presented to illustrate the performance of this adaptive observer.