How to Systematically Distribute Candidate Models and Robust Controllers in Multiple-Model Adaptive Control: A Coverage Control Approach

Distributing nominal models in multiple-models applications constitutes a long standing problem. The set of models needs to be distributed in such a way that their corresponding controllers can stabilize all possible system configurations in a large uncertainty set. This paper presents a systematic solution by phrasing the distribution as coverage control problem, in which each model covers a subset of the uncertainty. The subsets are derived based on a combination of the ν-gap metric, which serves as a distance measure, and the generalized stability margin. Characterizing coverage in terms of the ν-gap also motivates the use of H
_∞
controller synthesis to design a set of controllers. The proposed algorithms are initialized with suboptimal model configurations. Two update laws optimize the model parameters and minimize the coverage function. The first algorithm performs a gradient descent on the coverage function and the second algorithm performs pairwise optimizations. Due to computational complexity, a discretized implementation is derived, which reduces the optimization to an efficient graph search. The proposed algorithms are evaluated in numeric benchmark examples.