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对系统识别的最佳输入信号设计的近似贝叶斯方法
1Department of Automatic Control and Robotics, Faculty of Electrical Engineering, Automatics, Computer Science, and Biomedical Engineering, AGH University of Krakow, al. A. Mickiewicza 30, 30-059 Krakow, Poland.
Entropy (Basel, Switzerland)
|October 28, 2025
概括
本研究介绍了一种贝叶斯方法,使用相互信息 (MI) 来设计用于系统识别的信息输入信号. 该方法克服了计算挑战,并提高了准确性,特别是在模型不确定性方面.
科学领域:
- 控制系统工程 控制系统工程
- 统计推理 统计推理
- 信息理论 信息理论
背景情况:
- 经典系统识别依赖于费舍尔信息,费舍尔信息受到局部近似的限制,并与模型不确定性和非线性作斗争.
- 设计信息输入信号对于准确的系统识别至关重要,但传统方法存在局限性.
研究的目的:
- 开发一种强大的贝叶斯方法来设计用于系统识别的信息输入信号.
- 为解决与最大化信号设计的相互信息 (MI) 相关的计算挑战.
- 在存在模型不确定性和非线性时,提高系统识别准确性.
主要方法:
- 提出了贝叶斯框架,利用观察和参数之间的相互信息 (MI) 作为目标函数.
- 一个可处理的MI的下界被最大化,以克服计算难以处理.
- 开发了一种高效的算法,以减少反转大协同变量矩阵的计算复杂性,使其能够应用于长实验数据.
主要成果:
- 基于MI的建议贝叶斯方法被证明优于平均D-最佳设计和其他半贝叶斯方法.
- 开发的算法显著降低了计算负载,使贝叶斯式方法可用于长期系统识别.
- 该方法有效地设计输入信号,最大限度地获取信息,用于识别准线性随机动态系统.
结论:
- 使用相互信息的下界的贝叶斯方法为设计信息输入信号提供了一种强大而计算可行的方法.
- 这种技术提高了系统识别的准确性,特别是在具有模型不确定性和非线性复杂场景中.
- 该方法的有效性在各种应用中得到证明,包括原子传感器模型,强调其广泛的适用性和影响.
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