Initial Excitation Based Adaptive Observer With Multiple Switching

Adaptive observer design deals with online estimation of states using input-output information of a dynamical system in the presence of parametric uncertainty in the dynamics. It works with the principle of simultaneous estimation of states and the uncertain parameters using suitable online update routines to ensure stability of the estimation error dynamics. Conventional adaptive observers rely on the richness of input-output signals to satisfy the persistence of excitation (PE) condition for parameter convergence. The PE condition is restrictive since it demands sufficient energy of the signal for the entire time span and the condition depends on the future behavior of the signal, which poses difficulty in online verification. In contrast to conventional designs, the proposed work develops a switched adaptive observer which ensures uniformly ultimately bounded (UUB) stability of the estimation error dynamics without requiring the stringent PE condition, while imposing an online-verifiable condition of initial excitation (IE) on the regressor signal. The IE condition is significantly milder than PE, since it demands sufficient energy/richness of the signal only in the initial time-window. Strategic introduction of multiple switching in the parameter estimator ensures the ultimate bound to be arbitrarily reducible by appropriate choice of the design parameters.