Adaptive Mixing Control with Multiple Estimators∗

A recently proposed adaptive control scheme with mixing involves the use of precalculated candidate controllers whose output is weighted based on the parameter estimates generated by an on-line parameter estimator. It has been shown analytically and demonstrated in simulations that adaptive control with mixing exhibits good performance for the regulation case in the presence of modeling errors, disturbances and time delays. The transient performance however depends on the initial conditions of the parameter estimator and for some initial conditions the transient oscillations may not be acceptable in certain applications. In this paper we combine the controller mixing strategy with a multiple parameter estimation architecture plus a hysteresis switching logic selecting the parameter estimates that generate the smaller estimation errors to decide the mixing of the controllers. We show analytically that this approach, referred to as multi estimator adaptive mixing control (Multi-AMC), achieves stability and stability robustness and we demonstrate using extensive simulations that the scheme achieves consistently better transient performance than the original AMC. In addition we extend the design and analysis to be applicable to the tracking case where the output is required to track a non zero reference signal. The stability and performance of the proposed scheme in the presence of unmodeled dynamics and bounded disturbances has also been analyzed and demonstrated using a numerical example. Copyright c © 2011 John Wiley & Sons, Ltd.