On Space-Filling Input Design for Nonlinear Dynamic Model Learning: A Gaussian Process Approach

While optimal input design for linear systems has been well-established, no systematic approach exists for nonlinear systems where robustness to extrapolation/interpolation errors is prioritized over minimizing estimated parameter variance. To address this issue, we develop a novel space-filling input design strategy for nonlinear system identification that ensures data coverage of a given region of interest. By placing a Gaussian Process (GP) prior on the joint input-state space, the proposed strategy leverages the GP posterior variance to construct a cost function that promotes space-filling input design. Consequently, this enables maximization of the coverage in the region of interest, thereby facilitating the generation of informative datasets. Furthermore, we theoretically prove that minimization of the cost function implies the space-filling property of the obtained data. Effectiveness of the proposed strategy is demonstrated on both an academic and a mass-spring-damper example, highlighting its potential practical impact on efficient exploration of the dynamics of nonlinear systems.