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H∞control for Poisson-driven stochastic systems
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.amc.2020.125716
Bo Song , Ya Zhang , Ju H. Park

Abstract The paper aims to investigate the H ∞ control problem for systems perturbed by jump random noise, i.e., Poisson-driven stochastic systems (SSs). Firstly, this paper uses the Doob-Meyer decomposition and measure theory to give a model transformation method, and Poisson-driven SSs, which are SSs driven by semi-martingale, are transformed into SSs driven by compensated Poisson process. Since SSs driven by compensated Poisson process are SSs driven by martingale, we can use effective properties and tools in martingale theory to investigate the H ∞ control problem. Secondly, this paper utilizes martingale theory to deal with the jump item and the sum of stochastic integrals (SIs) with respect to (w.r.t.) the continuous part of states in Ito formula, and then gives an equivalent Ito formula for SDEs driven by compensated Poisson process. Thirdly, on the basis of these, this paper presents a simple H ∞ controller design method. Furthermore, the design criterion contains information about the average number of jump random events in a unit time, and one can utilize convex optimization algorithm to estimate the maximum average number of jump random events in a unit time, which the closed-loop system can tolerate to achieve the stability and H ∞ performance. Finally, the usefulness of the design result is verified by two numerical examples.

中文翻译:

泊松驱动随机系统的 H∞控制

摘要 本文旨在研究受跳跃随机噪声扰动的系统,即泊松驱动随机系统(SSs)的H ∞ 控制问题。首先,本文利用Doob-Meyer分解和测度理论给出了一种模型转换方法,将Poisson-driven SSs,即半鞅驱动的SSs转化为补偿泊松过程驱动的SSs。由于补偿泊松过程驱动的 SS 是由鞅驱动的 SS,我们可以利用鞅理论中的有效性质和工具来研究 H ∞ 控制问题。其次,本文利用鞅理论对Ito公式中状态的连续部分(wrt)处理跳跃项和随机积分(SI)的和,然后给出补偿泊松驱动的SDE的等价Ito公式过程。第三,在此基础上,本文提出了一种简单的H ∞ 控制器设计方法。此外,设计准则包含单位时间内跳跃随机事件的平均数量的信息,可以利用凸优化算法来估计闭环系统可以容忍的单位时间内跳跃随机事件的最大平均数量以实现稳定性和 H ∞ 性能。最后通过两个数值算例验证了设计结果的有效性。闭环系统所能容忍的,以实现稳定性和 H ∞ 性能。最后通过两个数值算例验证了设计结果的有效性。闭环系统所能容忍的,以实现稳定性和 H ∞ 性能。最后通过两个数值算例验证了设计结果的有效性。
更新日期:2021-03-01
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