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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 nonlinear system function using its Taylor's expansion is possible, this scheme provides an adaptation law to estimate such an approximation. With the help of a properly designed sampling rule, the neighborhood of approximation can be moved from time to time in order to capture the fast changing system dynamics. Several modifications are also made in the control law to avoid exciting the un-modelled dynamics, to reduce the noise sensitivity and to accommodate various signal levels in the system response. Performance and important features of the proposed controller are illustrated through simulations of some dynamic systems.