Optimal model distributions in supervisory adaptive control

Several classes of multi-model adaptive control schemes have been proposed in literature: instead of one single parameter-varying controller, in this adaptive methodology multiple fixed-parameter controllers for different operating regimes (i.e. different models) are utilised. Despite advances in multi-model adaptive control theory, the question of how the synthesis of the pairs model/controller will affect transient and steady-state performance is not completely addressed. In particular, it is not clear to which extent placing the pairs model/controller in a structurally optimal way will result in a relevant improvement of the properties of the switching algorithm. In this study the authors focus on a multi-model unfalsified adaptive supervisory switching control scheme, and they show how the minimisation of a suitable structural criterion can lead to improved performance of the adaptive scheme. The peculiarity of the resulting structural optimality criterion is that the optimisation is carried out so as to optimise the entire behaviour of the adaptive algorithm, i.e. both the learning transient and the steady-state response. This is in contrast to alternative multi-model adaptive control schemes, where special structural optimisation considers only the steady-state ideal response and neglects learning transients. A comparison with respect to model distributions achieved via two structural optimisation criteria is made via a benchmark example.