| 引用本文: | 张爽,李滚.输出约束条件下一类热传导方程的边界控制[J].控制理论与应用,2016,33(8):1068~1073.[点击复制] |
| Zhang Shuang,Li Gun.Boundary control for an inhomogeneous heat equation with output constraint[J].Control Theory and Technology,2016,33(8):1068~1073.[点击复制] |
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| 输出约束条件下一类热传导方程的边界控制 |
| Boundary control for an inhomogeneous heat equation with output constraint |
| 摘要点击 2856 全文点击 1577 投稿时间：2016-02-04 修订日期：2016-08-28 |
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| DOI编号 10.7641/CTA.2016.60074 |
| 2016,33(8):1068-1073 |
| 中文关键词 热传导方程 偏微分方程 边界控制 输出约束 分布参数控制系统 |
| 英文关键词 heat equation partial differential equations boundary control output constraint distributed parameter control systems |
| 基金项目 国家自然科学基金项目(61403063), 中央高校基本科研业务费项目(ZYGX2015J120)资助. |
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| 中文摘要 |
| 约束问题普遍存在于物理系统中, 如何解决分布参数系统的约束问题还没有有效的方法. 本文以一类非齐
次的热传导方程作为研究对象, 设计了一种新型的边界控制方法来稳定系统状态并解决热传导方程的约束问题. 为
此首先简要地介绍了由偏微分方程和常微分方程共同描述的热传导方程. 然后, 在未知的分布式外界扰动的影响
下, 设计一种新型的基于障碍–积分型李雅普诺夫函数的边界控制方法. 此方法是基于原始的分布参数系统模型,
没有任何的模型简化, 因此有效地避免了溢出不稳定问题. 本文采用李雅普诺夫方法证明系统稳定性并保证系统的
边界输出约束在一定的范围内. 最后采用有限差分法进行仿真验证, 仿真结果进一步证明了所提出的边界控制方法
的有效性. |
| 英文摘要 |
| Constrained problems are commonly existed in the physical system. Unfortunately there is no effective
way to solve the constrained problem for distributed parameter systems. In this paper, an inhomogeneous heat equation
is studied and a novel boundary control is designed to stabilize the system states and solve the constrained problem for
the heat equation. First, the heat equation described by partial differential equation (PDE)-ordinary differential equation
(ODE) is briefly introduced. Then, under the effect of unknown distributed disturbance, a novel barrier-integral Lyapunov
functional-based method is proposed. The designed method is based on the original distributed parameter system model
without any model simplification to avoid the spillover instability problem. Third, Lyapunov’s Direct Method is used to
analyze the stability of the closed-loop system and to ensure that the boundary output of the heat equation remains in a
constrained space. Finally, extensive simulations are given by using finite difference method. The simulation results further
show the effectiveness of the proposed control method. |