分布式时滞系统LQR最优控制问题的PI算法
PI Algorithm for LQR Optimal Control Problem of Distributed Time-Delay System
摘要: 本文将基于模型的策略迭代方法推广到了分布式时滞系统的线性二次最优控制问题(LQR)的求解，证明了由该迭代方法得到的性能指标是递减的，且控制器收敛于最优控制器。
Abstract: This paper extends the model-based policy iteration method to the solution of the Linear Quadratic Regulator (LQR) problem for distributed delayed systems. It is demonstrated that the performance criterion obtained through this iterative method is monotonically decreasing, and the controller converges to the optimal controller.
文章引用：陈甲敏, 孙小淇. 分布式时滞系统LQR最优控制问题的PI算法[J]. 理论数学, 2025, 15(2): 104-113. https://doi.org/10.12677/pm.2025.152052

参考文献

[1] 张菊. 自动化技术在机械设计制造中的应用实践[J]. 机械管理开发, 2022, 37(2): 308-309.
[2] 黄建峰. 自动化技术在机械设计制造中的应用价值[J]. 黑龙江科学, 2021, 12(22): 116-117.
[3] Kharitonov, V. (2012) Time-Delay Systems: Lyapunov Functionals and Matrices. Springer Science & Business Media.
[4] Kwakernaak, H. and Sivan, R. (1972) Linear Optimal Control Systems. Wiley-Interscience.
[5] Lancaster, P. and Rodman, L. (1995) Algebraic Riccati Equations. Oxford University Press, 504.
[6] Xie, L., Fridman, E. and Shaked, U. (2001) Robust H/Sub ∞/ Control of Distributed Delay Systems with Application to Combustion Control. IEEE Transactions on Automatic Control, 46, 1930-1935. [Google Scholar] [CrossRef] 
[7] Jiang, Y. and Jiang, Z. (2012) Computational Adaptive Optimal Control for Continuous-Time Linear Systems with Completely Unknown Dynamics. Automatica, 48, 2699-2704. [Google Scholar] [CrossRef] 
[8] Jiang, Z., Bian, T. and Gao, W. (2020) Learning-Based Control: A Tutorial and Some Recent Results. Foundations and Trends® in Systems and Control, 8, 176-284. [Google Scholar] [CrossRef] 
[9] Cui, L., Pang, B. and Jiang, Z. (2024) Learning-Based Adaptive Optimal Control of Linear Time-Delay Systems: A Policy Iteration Approach. IEEE Transactions on Automatic Control, 69, 629-636. [Google Scholar] [CrossRef] 
[10] Kleinman, D. (1968) On an Iterative Technique for Riccati Equation Computations. IEEE Transactions on Automatic Control, 13, 114-115. [Google Scholar] [CrossRef] 
[11] Ross, D.W. and Flügge-Lotz, I. (1969) An Optimal Control Problem for Systems with Differential-Difference Equation Dynamics. SIAM Journal on Control, 7, 609-623. [Google Scholar] [CrossRef] 
[12] Eidelman, Y., Milman, V. and Tsolomitis, A. (2004). Functional Analysis: An Introduction. American Mathematical Society.[CrossRef] 
[13] Burns, J.A., Sachs, E.W. and Zietsman, L. (2008) Mesh Independence of Kleinman-Newton Iterations for Riccati Equations in Hilbert Space. SIAM Journal on Control and Optimization, 47, 2663-2692. [Google Scholar] [CrossRef] 

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