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| A Stackelberg strategy for continuous-time mixed ${\rm H}_2/{\rm H}_\infty$ control problem with time delay |
| XiaoqianLI,WeiWANG,JuanjuanXU,HuanshuiZHANG |
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| (School of Control Science and Engineering, Shandong University, Jinan Shandong 250061, China) |
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| DOI：https://doi.org/10.1007/s11768-018-8014-4 |
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| 基金项目:This work was supported by the National Natural Science Foundation of China (Nos. 61633014, 61573220, 61573221) and the Fundamental Research Funds of Shandong University (No. 2017JC009). |
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| A Stackelberg strategy for continuous-time mixed ${\rm H}_2/{\rm H}_\infty$ control problem with time delay |
| Xiaoqian LI,Wei WANG,Juanjuan XU,Huanshui ZHANG |
| (School of Control Science and Engineering, Shandong University, Jinan Shandong 250061, China) |
| Abstract: |
| This paper is concerned with the mixed H2/H∞ control with linear continuous time system and time delay. To deal with
this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The
leader’s control strategy minimizes the cost function which is in H2 norm and the follower’s control strategy maximizes the cost
function which is in H∞ norm. The main technique of this paper is deal with the noncausal relationship of the variables caused
by time delay in the control input by introducing two costates to capture the future information and one state to capture the past
information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended
state space expression, the explicit expression of the strategy is obtained. |
| Key words: Mixed H2/H∞ control, continuous-time system, Stackelberg strategy, time delay |
