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Receding Horizon H_∞ Control for Input-Delayed Systems

机译：输入延迟系统的后退水平H_∞控制

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摘要

We propose the 'receding horizon H_∞ control (RHHC) for input-delayed systems. A new cost function for a finite horizon dynamic game problem is first introduced, which includes two terminal weighting terms parameterized by a positive definite matrix, called a terminal weighing matrix. Secondly, the RHHC is obtained from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the nonincreasing monotonicity. Finally, we show the asymptotic stability and H_∞ boundedness of the closed-loop system controlled by the proposed RHHC. The proposed RHHC has a guaranteed H_∞ performance bound for nonzero external disturbances and the quadratic cost can be improved by adjusting the prediction horizon length for nonzero initial condition and zero disturbance, which is not the case for existing memoryless state-feedback controllers. It is shown through a numerical example that the proposed RHHC is stabilizing and satisfies the infinite horizon H_∞ performance bound. Furthermore, the performance in terms of the quadratic cost is shown to be improved by adjusting the prediction horizon length when there exists no external disturbance with nonzero initial condition.
机译：我们提出了用于输入延迟系统的“后视水平H_∞控制（RHHC）”。首先介绍了一种用于有限水平动态博弈问题的新成本函数，其中包括由正定矩阵（称为终端权重矩阵）参数化的两个终端加权项。其次，RHHC是从有限动态博弈问题的解中获得的。第三，我们提出了一个LMI条件，在该条件下鞍点值满足非递增单调性。最后，我们显示了所提出的RHHC控制的闭环系统的渐近稳定性和H_∞有界性。所提出的RHHC对于非零外部干扰具有保证的H_∞性能界限，并且可以通过调整非零初始条件和零干扰的预测水平长度来改善二次成本，而对于现有的无记忆状态反馈控制器则不是这种情况。通过数值算例表明，所提出的RHHC是稳定的，并且满足无限地平线H_∞性能范围。此外，当不存在具有非零初始条件的外部干扰时，通过调整预测水平长度，可以提高以二次成本表示的性能。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第12期|927213.1-927213.15|共15页
  • 作者

    Han Woong Yoo; Soohee Han; Young Sam Lee;

  • 作者单位

    Delft Center for Systems and Control, Delft University of Technology, 2628 CD Delft, The Netherlands;

    Department of Electrical Engineering, Konkuk University, Seoul 143-701, Republic of Korea;

    School of Electrical Engineering, Inha University, Incheon 402-751, Republic of Korea;

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