线性分数阶系统的采样数据最优控制

中文摘要 AI 辅助

本文研究了阶数 $\alpha \in (0, 1]$ 的 Caputo 线性分数阶系统在连续时间状态约束和输入约束下的最优控制问题。由于状态约束施加于采样区间内而非仅在采样时刻，所产生的问题是半无限的。为解决这一问题，我们推导了采样间轨迹的采样数据表示，并利用 Bernstein 多项式构造连续时间状态约束的多胞形近似。我们获得了该近似引入的保守性的显式界。通过细分每个采样区间并在每个子区间上应用基于 Bernstein 的构造，近似可以任意紧密。数值算例说明了所提出包络的紧密性、所提出方法的计算可行性以及近似精度与计算复杂度之间的权衡。

英文摘要

This paper studies the problem of optimal control of Caputo linear fractional-order systems of order $α\in (0, 1]$ with continuous-time state constraints and input constraints. The resulting problems are semi-infinite, since the state constraints are imposed over the sampling intervals and not merely at the sampling instants. To address this, we derive a sampled-data representation of the inter-sample trajectory and use Bernstein polynomials to construct polytopic approximations of the continuous-time state constraints. Explicit bounds are obtained for the conservatism introduced by this approximation. By subdividing each sampling interval and applying the Bernstein-based construction on every subinterval, the approximation is made arbitrarily tight. Numerical examples illustrate the tightness of the proposed enclosures, the computational tractability of the proposed method, and the trade-off between approximation accuracy and computational complexity.

发表机构

• School of Electronics, Electrical Engineering, and Computer Science (EEECS)（电子、电气工程和计算机科学学院）
• Queen’s University Belfast（贝尔法斯特女王大学）

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