论文标题
Sobolev Norm中Schlögl方程的轨迹的全球稳定性
Global stabilizability to trajectories for the Schlögl equation in a Sobolev norm
论文作者
论文摘要
在强溶液的自然状态空间的规范中研究了Schlögl模型轨迹的稳定性，该溶液的自然状态空间的规范严格包含在平方集成函数的标准枢轴空间中。作为执行器，使用了有限数量的指标函数，并且控件输入将受到边界约束。提出了稳定的饱和反馈控制，其中执行器和输入结合的集合独立于靶向轨迹。此外，研究了开环的最佳稳定受限控制和相关的一阶最佳条件的存在。然后将这些条件用于计算基于水平的对照稳定。给出了数值模拟的结果，将其稳定性能与饱和的显式反馈控制的结果进行了比较。
The stabilizability to trajectories of the Schlögl model is investigated in the norm of the natural state space for strong solutions, which is strictly contained in the standard pivot space of square integrable functions. As actuators a finite number of indicator functions are used and the control input is subject to a bound constraint. A stabilizing saturated explicit feedback control is proposed, where the set of actuators and the input bound are independent of the targeted trajectory. Further, the existence of open-loop optimal stabilizing constrained controls and related first-order optimality conditions are investigated. These conditions are then used to compute stabilizing receding horizon based controls. Results of numerical simulations are presented comparing their stabilizing performance with that of saturated explicit feedback controls.
