Finite Horizon Discrete-Time Adaptive Dynamic Programming

有限时域离散时间自适应动态规划

• 批准号: 0621694
• 负责人: Derong Liu
• 金额: $ 24万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0621694&HistoricalAwards=false
• 关键词: Finite; Horizon; Discrete; Time; Adaptive

Finite Horizon Discrete-Time Adaptive Dynamic ProgrammingDerong Liu, University of Illinois at ChicagoThe objective of the present project is to make fundamental contributions to the field of intelligent control. In particular, the PI will conduct adaptive dynamic programming research under the following three topics. The first topic is about the analysis of optimal controllers and optimal performance costs under the condition that the number of steps for performing optimal control of nonlinear discrete-time systems is not fixed but is known to be finite. The second topic is to develop adaptive neural dynamic programming algorithms for the optimal control of nonlinear discrete-time systems. The third topic is to establish the stability, convergence, and optimality theory for the adaptive dynamic programming algorithms developed in this project. The first topic is the foundation of the second topic. The third topic provides guarantees of stability, convergence and optimality when applying our adaptive neural dynamic programming algorithms. The second topic is the ultimate goal of this project. The PI will develop stable and convergent algorithms for adaptive dynamic programming of nonlinear discrete-time systems.Intellectual MeritThe PI will investigate adaptive dynamic programming for discrete-time nonlinear systems. Specifically, for discrete-time optimal control problems with finite, but may not be fixed, time horizon, he will establish analysis results of optimal controllers for each control step and investigate properties of these controllers, in order to build a foundation for neural network implementation of adaptive dynamic programming. The main goal of this project is to develop adaptive neural dynamic programming algorithms for nonlinear discrete-time systems. Since the algorithms will be implemented using neural networks, the PI can find the minimum of cost function without solving partial differential equations. Broader Impacts In addition to training Ph.D. students, the PI will work with several undergraduate students on research topics in the present project in the next three years. In the present project, The PI will continue his effort in recruiting minority undergraduate students to his research program. It is believed that the success of the present project will build a solid foundation for adaptive dynamic programming of nonlinear discrete-time systems with finite time horizon. Theoretical results obtained in the present project will help push forward practical applications of adaptive dynamic programming in the years to come.

有限时域离散时间自适应动态规划刘德荣，伊利诺伊大学芝加哥分校本项目的目标是为智能控制领域做出基础性贡献。特别是，PI将在以下三个主题下进行自适应动态规划研究。第一个主题是关于最优控制器和最优性能成本的条件下，执行非线性离散时间系统的最优控制的步骤数是不固定的，但已知是有限的分析。第二个主题是发展非线性离散时间系统最优控制的自适应神经动态规划算法。第三个主题是建立稳定性，收敛性和最优性理论的自适应动态规划算法在这个项目中开发。第一个主题是第二个主题的基础。第三个主题提供了保证的稳定性，收敛性和最优性时，应用我们的自适应神经动态规划算法。第二个主题是这个项目的最终目标。PI将为非线性离散时间系统的自适应动态规划开发稳定和收敛的算法。智力MeritThe PI将研究离散时间非线性系统的自适应动态规划。具体而言，对于离散时间最优控制问题，有限，但可能不是固定的时间范围，他将建立每个控制步骤的最优控制器的分析结果，并研究这些控制器的属性，以建立神经网络实现自适应动态规划的基础。本计画的主要目标是发展非线性离散时间系统的适应性类神经动态规划演算法。由于算法将使用神经网络来实现，PI可以找到成本函数的最小值，而无需求解偏微分方程。除了培养博士学位外，鉴于学生人数众多，PI将在未来三年内与几名本科生合作研究本项目的研究课题。在目前的项目中，PI将继续努力招募少数民族本科生参加他的研究计划。相信本课题的成功将为有限时域非线性离散时间系统的自适应动态规划奠定坚实的基础。本研究所取得的理论成果将有助于推动自适应动态规划在未来几年的实际应用。