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| Reduction of data amount in data-driven design of linear quadratic regulators |
| ShinsakuIzumi1,XinXin2 |
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| (1 School of Systems Engineering, Kochi University of Technology, Kami, Kochi 782-8502, Japan;2 School of Automation, Southeast University, and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing 210096, Jiangsu, China) |
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| 摘要: |
| This paper discusses the data-driven design of linear quadratic regulators, i.e., to obtain the regulators directly from experimental
data without using the models of plants. In particular, we aim to improve an existing design method by reducing
the amount of the required experimental data. Reducing the data amount leads to the cost reduction of experiments and
computation for the data-driven design. We present a simplified version of the existing method, where parameters yielding
the gain of the regulator are estimated from only part of the data required in the existing method. We then show that the
data amount required in the presented method is less than half of that in the existing method under certain conditions. In
addition, assuming the presence of measurement noise, we analyze the relations between the expectations and variances of
the estimated parameters and the noise. As a result, it is shown that using a larger amount of the experimental data might
mitigate the effects of the noise on the estimated parameters. These results are verified by numerical examples. |
| 关键词: Data-driven design · Linear quadratic regulators · Linear systems · Riccati equation · Stochastic properties |
| DOI：https://doi.org/10.1007/s11768-024-00220-y |
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| 基金项目: |
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| Reduction of data amount in data-driven design of linear quadratic regulators |
| Shinsaku Izumi1,Xin Xin2 |
| (1 School of Systems Engineering, Kochi University of Technology, Kami, Kochi 782-8502, Japan;2 School of Automation, Southeast University, and Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Nanjing 210096, Jiangsu, China) |
| Abstract: |
| This paper discusses the data-driven design of linear quadratic regulators, i.e., to obtain the regulators directly from experimental
data without using the models of plants. In particular, we aim to improve an existing design method by reducing
the amount of the required experimental data. Reducing the data amount leads to the cost reduction of experiments and
computation for the data-driven design. We present a simplified version of the existing method, where parameters yielding
the gain of the regulator are estimated from only part of the data required in the existing method. We then show that the
data amount required in the presented method is less than half of that in the existing method under certain conditions. In
addition, assuming the presence of measurement noise, we analyze the relations between the expectations and variances of
the estimated parameters and the noise. As a result, it is shown that using a larger amount of the experimental data might
mitigate the effects of the noise on the estimated parameters. These results are verified by numerical examples. |
| Key words: Data-driven design · Linear quadratic regulators · Linear systems · Riccati equation · Stochastic properties |
