ADAPTIVE EXPONENTIAL TRACKING FOR NONLINEARLY PERTURBED MINIMUM-PHASE SYSTEMS

The class of systems under consideration consists of multi-input, multi-output, finite dimensional, state space systems subject to nonlinearities in the input-, state- and output-variables and of unmodeled systems dynamics. The systems and its state dimension are not known precisely. However, structural information is assumed, such as the linear system is minimum phase, the spectrum of the high-frequency gain matrix lies either in the open right- or left-half plane. For different classes of systems, simple adaptive high-gain stabilizers-not based on identification or estimation algorithms-are presented, which, in the presence of certain nonlinearities, ensure exponential decay of the motion of the closed-loop system and finite gain convergence of the parameters of the adaptive controllers. Using these results in cooperation with an internal model, an adaptive tracking controller, which guarantees exponential decay of the error between the output and reference signals belonging to a known solution space of a differential equation, is presented for linear systems.