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This chapter describes in detail how stochastic data-driven approaches can be employed to define the centers underlying a native space-based approach to the design of adaptive control systems for deterministic, continuous-time ordinary differential equations. Leveraging some key properties of native spaces, this chapter characterizes the ultimate bounds on the closed-loop trajectory tracking error. These bounds are explicit functions of the dimension of the approximating hypothesis space and the number of samples employed to estimate the matched functional uncertainty. Numerical examples demonstrate the applicability of these approaches in a learn-then-control and a switched learn-and-control framework.

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Data-Driven Methods and Adaptive Control: Stochastic Analysis

  • 章节

  • 发表日期：

    2025年

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  • Andrew J. Kurdila,
  • Andrea L’Afflitto,
  • John A. Burns

摘要

This chapter describes in detail how stochastic data-driven approaches can be employed to define the centers underlying a native space-based approach to the design of adaptive control systems for deterministic, continuous-time ordinary differential equations. Leveraging some key properties of native spaces, this chapter characterizes the ultimate bounds on the closed-loop trajectory tracking error. These bounds are explicit functions of the dimension of the approximating hypothesis space and the number of samples employed to estimate the matched functional uncertainty. Numerical examples demonstrate the applicability of these approaches in a learn-then-control and a switched learn-and-control framework.