Reduced-Order Gaussian Processes for Partially Unknown Nonlinear Control Systems

• 成果类型: Article
• 署名作者: Awan, Asad Ullah; Zamani, Majid
• 署名单位: Technical University of Munich; University of Munich; University of Colorado System; University of Colorado Boulder
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3564219
• 发表日期: 2025
• 页码: 6893-6900
• 关键词: VECTORS; kernel; Symmetric matrices; SYMBOLS; Jacobian matrices; Hilbert space; Adaptation models; trajectory; mathematical models; Gaussian Processes; control systems; Control system synthesis; data-driving modeling; Dimensionality Reduction; mathematics; Modeling; statistics; Stochastic processes; systems theory and engineering

摘要

In this work, we develop a scheme for constructing continuous approximations (referred to as abstractions) of a class of discrete-time control systems with partially unknown dynamics. The abstraction, itself a nonlinear discrete-time control system (preferably with a significantly lower dimension than the original one) can be used as a substitute in the controller design process. The technique consists of using data sampled from the concrete system to find a lower dimensional subspace of its state space (which we call the active subspace), and constructing an abstraction candidate using Gaussian process (GP) regression. We derive sufficient conditions under which the GP candidate is shown to be the abstraction of the original system while quantifying the error bound between the output of the abstraction and that of the concrete system. A numerical example is presented to illustrate the effectiveness of this approach.