Control of travelling and rotating waves in spatially extended nonlinear systems (B06)

我们的目标是控制主动媒体中的自组织时空模式。具体地说，我们根据给定的二维和三维区域内的运动协议来引导非线性波和移动局部光点。为了达到我们的控制目标，我们将基于多尺度摄动理论的方法应用于位置和形状控制，并利用了包括稀疏控制和逐点状态约束在内的偏微分方程组的强大的最优控制方法。此外，我们还研究了空间限制对波和光斑动力学的影响，并研究了小空间中的反应扩散过程。

We aim at controlling self-organized spatio-temporal patterns in active media. In particular, we guide non-linear waves and moving localized spots according to a given protocol of movement within two- and three-dimensional domains. To reach our control goals we apply methods based on multiple scale perturbation theory for position and shape control and exploit the powerful methods of optimal control of partial differential equations including sparse control and pointwise state constraints. Additionally, we investigate the impact of spatial confinement on wave and spot dynamics and study reaction-diffusion processes in small compartments.