论文标题
在Neumann驱动下，基于1D热方程的基于有限维观察者的延迟。
Delayed finite-dimensional observer-based control of 1D heat equation under Neumann actuation
论文作者
论文摘要
最近，引入了一种建设性方法，用于基于有限维观察者对1D抛物线PDE的控制。在本文中，我们提出了一种改进的方法，以减少的LMI（大大缩短了计算时间），并引入预测因子以使用较大的延迟进行管理。我们处理尚未研究的Neumann致动和非本地测量的一维热方程式的情况。我们应用模态分解，并通过直接Lyapunov方法证明$ l^2 $指数稳定性。我们提供降低的LMI条件，以查找观察者尺寸$ n $和产生的衰减率。 LMI尺寸不会随$ n $而增长。 LMI对于大$ n $总是可行的，对于$ n $的可行性意味着$ n+1 $的可行性。在存在快速变化（在延迟衍生上没有任何约束的）输入和输出延迟的情况下，我们首次通过延迟实现控制器的实现。为了通过较大的延迟进行管理，我们构建了基于经典观察者的预测指标。对于已知的输入延迟，LMIS尺寸不会以$ n $增长，而对于未知的LMIS尺寸增长，但比现有结果中的尺寸较小。一个数值示例证明了我们方法的效率。
Recently a constructive method was introduced for finite-dimensional observer-based control of 1D parabolic PDEs. In this paper we present an improved method in terms of the reduced-order LMIs (that significantly shorten the computation time) and introduce predictors to manage with larger delays. We treat the case of a 1D heat equation under Neumann actuation and non-local measurement, that has not been studied yet. We apply modal decomposition and prove $L^2$ exponential stability by a direct Lyapunov method. We provide reduced-order LMI conditions for finding the observer dimension $N$ and resulting decay rate. The LMI dimension does not grow with $N$. The LMI is always feasible for large $N$, and feasibility for $N$ implies feasibility for $N+1$. For the first time we manage with delayed implementation of the controller in the presence of fast-varying (without any constraints on the delay-derivative) input and output delays. To manage with larger delays, we construct classical observer-based predictors. For the known input delay, the LMIs dimension does not grow with $N$, whereas for unknown one the LMIs dimension grows, but it is ssentially smaller than in the existing results. A numerical example demonstrates the efficiency of our method.
