Abstract We consider distributed control of a class of 1-D parabolic PDEs under distributed in-domain point actuation and measurements in the presence of control constraints. This class includes unstable diffusion-reaction equations as well as stable Burgers’ equations, where we aim to locally improve the convergence. We suggest an observer-based control law that employs the averaged values of the observer state. This allows to regionally stabilize the system. We derive linear matrix inequalities (LMIs) conditions that provide an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example validates the efficiency of the method.

中文翻译：

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使用空间传感和驱动中的采样对一维抛物线偏微分方程进行约束控制

摘要 我们考虑在存在控制约束的情况下分布式域内点驱动和测量下的一类一维抛物线偏微分方程的分布式控制。此类包括不稳定的扩散反应方程以及稳定的 Burgers 方程，我们的目标是局部改进收敛性。我们建议使用观察者状态的平均值的基于观察者的控制律。这允许区域性地稳定系统。我们推导出线性矩阵不等式 (LMI) 条件，这些条件提供对初始条件集的估计，系统的状态轨迹从这些初始条件开始呈指数收敛到零。数值例子验证了该方法的有效性。