TRANSIENT PERFORMANCE AND ROBUSTNESS OF DIRECT ADAPTIVE-CONTROL

A direct adaptive controller with gradient estimator and parameter projection exhibits finite gain stability. To achieve this result, it is sufficient to assume that the modeled part of the plant is stably invertible (the real plant may have unstable zeros), that the external disturbances are bounded, and that the closed-loop transfer function from the reference to the tracking error of an optimized, reduced order system has small gain. In the ideal case, the gain of this transfer function equals zero; and with no external disturbances and fast adaptation, the system state converges exponentially fast to zero without assuming persistent excitation. The exponential decay property is lost when the adaptation is slowed down or nonzero reference signals are introduced. This may lead to long transients and slow convergence. In the nonideal case, the extended plant state converges to a limit set which may contain one or more chaotic attractors. The rate of convergence to an overbounding set, l(infinity) and l2 performance bounds are estimated. The l(infinity) performance deteriorates while the l2 performance improves as the (local) rate of adaptation is decreased.