Towards data-centric input signal design using sparse polynomial optimization

Data-centric approaches such as Model-on-Demand (MoD) generate a local linear model online from a database of regressors at a given operating point. This paper explores the use of sparse polynomial optimization methods to solve previously developed input signal design formulations for data-centric system identification methods. These formulations aim to develop sufficient support in the regressor space by addressing the optimal distribution of regressors. The resulting problems are posed as general polynomial optimization problems and the paper analyzes conditions on the objective and constraints which allows for tractable representation using sparse polynomials. It is shown that the input constraint set is sparse while the regressor distances are dense; towards that a reformulation is proposed to incorporate only selective regressor distance pairs to induce sparsity. A numerical example highlights the benefit of the proposed method.