Evaluation of identifier based and & non-identifier based adaptive supervisory & control using a benchmark example

Several classes of identifier and non-identifier based adaptive control schemes using a supervisory switching logic have been proposed in the literature. These schemes are based on different assumptions and claim to guarantee certain stability and performance properties. The purpose of this paper is to clarify what each algorithm guarantess in theory and how it performs in simulations. The identifier based schemes: Robust Multiple Model Adaptive Control (RMMAC) and Adaptive Mixing Control (AMC) and the non-identifier based schemes: Unfalsified Adaptive Switching Control (UASC) and Multi-model Unfalsified Adaptive Switching Control (MUASC). For each scheme we present the basic features of the algorithm and state the stability and performance guaranteed in theory. The benchmark example of is used to test the stability and performance properties of the schemes considered using extensive simulations. Our results show that the identifier based schemes require some knowledge about the plant whereas the non identifier based do not. The identifier based schemes however typically perform better than non-identifier based schemes when all the plant assumptions are satisfied, and can guarantee, from a theory viewpoint, at least for the AMC scheme, transient and asymptotic performance. The main positive feature the UASC and MUASC schemes is that, even in the absence of any prior information on the uncertain plant, they can select in finite time a final controller yielding, a finite affine gain from the reference to the data, under the minimal conceivable requirement, viz. the existence of a stabilizing candidate controller in the candidate controller set.