Energy control of distributed parameter systems via speed-gradient method: case study of string and sine-Gordon benchmark models
Energy control of distributed parameter systems via speed-gradient method: case study of string and sine-Gordon benchmark models
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通过速度梯度方法进行分布参数系统的能量控制：弦和正弦戈登基准模型的案例研究
DOI：
10.1080/00207179.2016.1260160
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发表时间：
2017
影响因子：
2.1
通讯作者：
B. Andrievsky
中科院分区：
文献类型：
--
作者：
Y. Orlov;Alexander L. Fradkov;B. Andrievsky
本文分析了无限维系统的能量控制问题。选取了基准线性波动方程和非线性sine-Gordon方程进行阐述。被认为是相对简单的情况下，分布均匀的空间控制。提出了哈密顿系统能量控制的速度梯度法。Fradkov在1996年提出的方法已经成功地应用于许多非线性和自适应控制问题，目前已经发展并证明了上述偏微分方程（PDE）的有效性。一个无限维版本的Krasovskiii-LaSalle原理验证所产生的闭环系统。通过应用这一原则，闭环轨迹示出要么接近所需的能量水平集或收敛到系统平衡。底层闭环系统的数值研究揭示了合理快速的瞬态过程和所需的能量水平的可行性，如果初始化与较低的能量水平。
ABSTRACT Energy control problems are analysed for infinite dimensional systems. Benchmark linear wave equation and nonlinear sine-Gordon equation are chosen for exposition. The relatively simple case of distributed yet uniform over the space control is considered. The speed-gradient method for energy control of Hamiltonian systems proposed by A. Fradkov in 1996, has already successfully been applied to numerous nonlinear and adaptive control problems is presently developed and justified for the above partial differential equations (PDEs). An infinite dimensional version of the Krasovskii–LaSalle principle is validated for the resulting closed-loop systems. By applying this principle, the closed-loop trajectories are shown to either approach the desired energy level set or converge to a system equilibrium. The numerical study of the underlying closed-loop systems reveals reasonably fast transient processes and the feasibility of a desired energy level if initialised with a lower energy level.