Adaptive control of nonlinear, uncertain systems using local function estimation

An adaptive control scheme is proposed for controlling a certain class of nonlinear, uncertain systems. When a local approximation of the system function using its Taylor's expansion is possible, this scheme provides an adaptation law to estimate such an approximation. With a proper sampling rule, the neighborhood of approximation can be moved from time to time in order to capture the fast changing system dynamics. Practical implementation issues are also considered to avoid exciting the unmodeled dynamics, to reduce the noise sensitivity, and accommodate the various signal levels in the system response. The important features and performance of the proposed controller are illustrated through simulations and experimental results associated with a magnetic bearing system.