论文标题

时空随机优化:理论和最佳控制和共同设计的应用

Spatio-Temporal Stochastic Optimization: Theory and Applications to Optimal Control and Co-Design

论文作者

Evans, Ethan N., Kendall, Andrew P., Boutselis, George I., Theodorou, Evangelos A.

论文摘要

对控制社区中部分微分方程(PDE)描述的时空系统的兴趣不大。这些系统不仅具有挑战性的控制,而且其致动的尺寸和放置本身就是一个NP困难的问题。最新方法要么在优化之前离散空间,要么在限制性线性假设下应用线性系统理论的工具。在这项工作中,我们将控制和执行器的放置视为一个耦合的优化问题,并在Hilbert空间上为非线性PDE提供了优化算法,并具有对白噪声的加法时空描述。我们研究一阶和二阶系统,并在此过程中将几个结果扩展到二阶PDE的情况。所描述的方法基于变异优化,并对反馈控制定律和执行器设计进行了连接的RL型优化。我们通过对各种SPDE的几个模拟实验证明了该方法的功效。

There is a rising interest in Spatio-temporal systems described by Partial Differential Equations (PDEs) among the control community. Not only are these systems challenging to control, but the sizing and placement of their actuation is an NP-hard problem on its own. Recent methods either discretize the space before optimziation, or apply tools from linear systems theory under restrictive linearity assumptions. In this work we consider control and actuator placement as a coupled optimization problem, and derive an optimization algorithm on Hilbert spaces for nonlinear PDEs with an additive spatio-temporal description of white noise. We study first and second order systems and in doing so, extend several results to the case of second order PDEs. The described approach is based on variational optimization, and performs joint RL-type optimization of the feedback control law and the actuator design over episodes. We demonstrate the efficacy of the proposed approach with several simulated experiments on a variety of SPDEs.

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