Adaptive Observer Design for Nonlinear Interconnected Systems With Applications

In this chapter, observers are designed for a class of nonlinear interconnected systems with uncertain TVPs, in which both the isolated subsystems and the interconnections are nonlinear. The designed observers are variable structure interconnected systems, but may not result in sliding motion. Under the condition that the difference between the unknown TVPs and the corresponding uncertain nominal values are bounded by constants, adaptive updating laws are proposed to estimate the parameters. The persistence of excitation conditions is not required. A set of sufficient conditions are proposed such that the error dynamics formed by the system states and the designed observers are asymptotically stable, while the parameters’ estimation errors are uniformly, ultimately bounded using the LaSalle’s theorem. The results obtained are applied to a coupled inverted pendulum system, and simulation results are presented to demonstrate the effectiveness and feasibility of the developed results. The main contribution includes: (i) Both the interconnections and isolated subsystems take nonlinear forms. (ii) The unknown parameters considered in the system are time varying, and the corresponding nominal values are not required to be known. (iii) The asymptotic convergence of the observation error between the states of the considered systems and the states of the designed observers is guaranteed; while the estimate errors of the TVPs are uniformly, ultimately bounded.