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迭代路径积分方法对非线性随机最优控制

Iterative Path Integral Method for Nonlinear Stochastic Optimal Control
课程网址: http://videolectures.net/cyberstat2012_satoh_optimal_control/  
主讲教师: Satoshi Satoh
开课单位: 广岛大学
开课时间: 2012-10-16
课程语种: 日语
中文简介:
到目前为止，我们一直在研究非线性随机控制。例如，在[1,2,3]中，我们提出了一种基于物理系统性质的渐近稳定方法，如一类非线性随机系统的无源性和不变性。此外，在[4,5]中，我们提出了一个随机有界稳定控制器，它使得工厂系统的状态以给定概率和状态界限的概率为界。本次演讲的主题是非线性最优控制，我想介绍我们最近与Bert Kappen教授一起研究的关于路径积分随机最优控制方法的扩展。将非线性随机最优控制问题简化为求解随机Hamilton Jacobi Bellman（SHJB）方程。然而，解决SHJB方程通常很困难，因为它是二阶非线性PDE。 Kappen [6]提出的路径积分方法为基于统计物理方法的一类非线性随机最优控制问题的SHJB方程提供了有效的解决方案。尽管此方法非常有用，但此方法中所需的某些假设限制了其应用。为了解决这个问题，我们在报告中提出了路径积分方法的迭代解决方案[7]。所提出的方法迭代地求解SHJB方程而不强加在常规方法中必需的假设。因此，它使我们能够基于路径积分方法解决更广泛的随机最优控制问题。由于所提出的方法在假设成立时减少到传统方法，因此被认为是传统结果的自然延伸。此外，我们研究了该算法的收敛性。[1] S. Satoh和K. Fujimoto，“关于随机端口哈密顿系统的无源性控制”，Proc。第47届IEEE会议on Decision and Control，2008，pp.4951 4956。\\ [2]，“基于无源性的随机端口哈密顿系统控制”，Trans。仪器和控制工程师协会，第一卷。 44，不。 8，pp.670 677,2008，（日文）。\\ [3]，“基于随机无源性的时变随机端口哈密顿系统的稳定性”，Proc。 IFAC Symp。非线性控制系统，2010，pp.611 616。\\ [4]，“基于观测器的机械系统随机轨迹跟踪控制”，Proc。 ICROS SICE Int。联合会议2009年，2009年，第1244 1248页。[5] S. Satoh和M. Saeki，“有界稳定的一类随机港哈密顿系统”，在Proc。第20届Symp。网络与系统的数学理论，2012，pp。（CD ROM）0150。\\ [6] H. J. Kappen，“最优控制理论的路径积分与对称破缺”，J。统计力学：理论与实验，p。 P11011,2005。\\ [7] S. Satoh，H.J。Kappen和M. Saeki，“基于路径积分的非线性随机最优控制的解决方法”，Proc。第12届SICE系统集成部年度会议，2012年，第7页。 P0194，（日文）。
课程简介: So far, we have been studying nonlinear stochastic control. For example, in [1, 2, 3], we have proposed an asymptotically stabilization method based on properties of physical systems such as passivity and invariance for a class of nonlinear stochastic systems. Besides, in [4, 5], we have proposed a stochastic bounded stabilization controller, which renders the state of the plant system bounded in probability for given probability and bounds of the state. The main subject of this talk is nonlinear optimal control, and I would like to introduce our recent research with Prof. Bert Kappen, on extension of the path integral stochastic optimal control method. Nonlinear stochastic optimal control problem is reduced to solving the stochastic Hamilton- Jacobi-Bellman (SHJB) equation. However, it is generally quite difficult to solve the SHJB equation, because it is a second-order nonlinear PDE. The path integral method proposed by Kappen [6] provides an efficient solution for a SHJB equation corresponding to a class of nonlinear stochastic optimal control problems, based on statistical physics approach. Although this method is very useful, some assumptions required in this method restrict its application. To solve this problem, we have proposed an iterative solution for the path integral method in our report [7]. The proposed method solves the SHJB equation iteratively without imposing the assumptions, which are necessary in the conventional method. Consequently, it enables us to solve a wider class of stochastic optimal control problems based on the path integral approach. Since the proposed method reduces to the conventional method when the assumptions hold, it is considered to be a natural extension of the conventional result. Furthermore, we investigate a convergence property of the algorithm.\\ [1] S. Satoh and K. Fujimoto, "On passivity based control of stochastic port-Hamiltonian systems," in Proc. 47th IEEE Conf. on Decision and Control , 2008, pp. 4951-4956.\\ [2] --, "Passivity based control of stochastic port-Hamiltonian systems," Trans. the Society of Instrument and Control Engineers, vol. 44, no. 8, pp. 670-677, 2008, (in Japanese).\\ [3] --, "Stabilization of time-varying stochastic port-Hamiltonian systems based on stochastic passivity," in Proc. IFAC Symp. Nonlinear Control Systems, 2010, pp. 611-616.\\ [4] --, "Observer based stochastic trajectory tracking control of mechanical systems," in Proc. ICROS-SICE Int. Joint Conf. 2009, 2009, pp. 1244-1248. \\ [5] S. Satoh and M. Saeki, "Bounded stabilization of a class of stochastic port-Hamiltonian systems," in Proc. 20th Symp. Mathematical Theory of Networks and Systems, 2012, pp. (CD-ROM) 0150.\\ [6] H. J. Kappen, "Path integrals and symmetry breaking for optimal control theory," J. Statistical Mechanics: Theory and Experiment, p. P11011, 2005.\\ [7] S. Satoh, H. J. Kappen, and M. Saeki, "A solution method for nonlinear stochastic optimal control based on path integrals," in Proc. 12th SICE System Integration Division Annual Conf., 2012, p. P0194, (in Japanese).
关 键 词: 非线性随机控制; 渐近稳定方法; 稳定控制器; 路径积分
课程来源: 视频讲座网
最后编审: 2019-03-13：lxf
阅读次数: 103

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