Heuristic Dynamic Programming Algorithm for Optimal Control Design of Linear Continuous-Time Hyperbolic PDE Systems
Heuristic Dynamic Programming Algorithm for Optimal Control Design of Linear Continuous-Time Hyperbolic PDE Systems
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DOI：
10.1021/ie300897m
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发表时间：
2012-07
影响因子：
4.2
通讯作者：
Huai‐Ning Wu;Biao Luo
中科院分区：
文献类型：
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作者：
Huai‐Ning Wu;Biao Luo
本文研究了具有部分未知系统动态的线性连续时间双曲型偏微分方程系统的最优控制问题。为了尊重的无限维性质的双曲型偏微分方程系统，该问题可以减少到寻找一个解决方案的空间相关的Riccati微分方程（SDRDE），这需要完整的系统模型。为此，提出了一种启发式动态规划（HDP）算法，该算法在线采集沿着系统轨迹的数据，学习SDRDE的解，而不需要系统的内部动态特性，从而实现双曲PDE系统的在线最优控制. HDP算法的收敛性是通过证明HDP算法产生一致收敛于SDRDE的解的非减序列来建立的。为了实现的目的，HDP算法是通过开发一个近似的方法的基础上加权残差的方法来实现。最后，蒸汽夹套管式换热器的应用证明了所开发的控制方法的有效性。
This work considers the optimal control problem of linear continuous-time hyperbolic partial differential equation (PDE) systems with partially unknown system dynamics. To respect the infinite-dimensional nature of the hyperbolic PDE system, the problem can be reduced to finding a solution of the space-dependent Riccati differential equation (SDRDE), which requires the full system model. Therefore, a heuristic dynamic programming (HDP) algorithm is proposed to achieve online optimal control of the hyperbolic PDE system, which online collects data accrued along system trajectories and learns the solution of the SDRDE without requiring the internal system dynamics. The convergence of HDP algorithm is established by showing that the HDP algorithm generates a nondecreasing sequence which uniformly converges to the solution of the SDRDE. For implementation purposes, the HDP algorithm is realized by developing an approximate approach based on the method of weighted residuals. Finally, the application on a steam-jacketed tubular heat exchanger demonstrates the effectiveness of the developed control approach.