Institut für Theoretische Physik, EW 7-1, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
Phys Rev Lett. 2014 Apr 11;112(14):148305. doi: 10.1103/PhysRevLett.112.148305. Epub 2014 Apr 10.
We present a method to control the position as a function of time of one-dimensional traveling wave solutions to reaction-diffusion systems according to a prespecified protocol of motion. Given this protocol, the control function is found as the solution of a perturbatively derived integral equation. Two cases are considered. First, we derive an analytical expression for the space (x) and time (t) dependent control function f(x,t) that is valid for arbitrary protocols and many reaction-diffusion systems. These results are close to numerically computed optimal controls. Second, for stationary control of traveling waves in one-component systems, the integral equation reduces to a Fredholm integral equation of the first kind. In both cases, the control can be expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed knowledge of the reaction kinetics unnecessary.
我们提出了一种根据预定运动方案来控制反应-扩散系统中一维行波解随时间变化的位置的方法。根据该方案，控制函数是由微扰推导出的积分方程的解。考虑了两种情况。首先，我们为任意协议和许多反应-扩散系统推导出了空间（x）和时间（t）相关控制函数 f(x,t)的解析表达式，该表达式在数值计算的最优控制附近。其次，对于单组分系统中行波的静态控制，积分方程简化为第一类弗雷德霍姆积分方程。在这两种情况下，控制可以表示为未受控制的波型及其传播速度，从而不需要详细了解反应动力学。
