Implicit Learning-Based Optimal Control of Uncertain Nonlinear Systems

不确定非线性系统基于隐式学习的最优控制

• 批准号: 0901491
• 负责人: Warren Dixon
• 金额: $ 30万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901491&HistoricalAwards=false
• 关键词: Implicit; Learning; Based; Optimal; Control

A SummaryProject Summary: This project focuses on the synthesis of new implicit learning-based methods thatcan optimally achieve some control objective for an uncertain nonlinear system. The main research goalsinclude the development and experimental verification of implicit learning and adaptive methods that enablethe mismatch between the desired and actual response of an uncertain nonlinear system to convergewhile optimizing a trade-off between performance and control energy. Efforts will investigate if differentlearning and adaptive methods have properties that yield more optimal solutions or lead to improved stabilitymargins. Progress on this research topic has been stymied by the challenge of solving a Hamilton-Jacobiequation, and the lack of mathematical tools to asymptotically compensate for generic disturbances with acontinuous controller. With the emergence of new implicit learning methods and general Lyapunov analysistechniques, the community is now well positioned to focus increasing attention on simultaneously achievingoptimality and stability for uncertain nonlinear systems. The learning capacity of the developed controllerswill enable analytical optimal control solutions for a broader class of engineering systems than is currentlypossible. Optimizing the performance of a control system along with the required control effort will yieldimproved efficiency that can lead to timely economic and environmental cost savings.Intellectual Merit: Few mathematical tools exist to synthesize controllers for nonlinear systems with modeluncertainty and unmodeled disturbances. Of the few tools that exist, either the developed controller requiresdiscontinuous feedback or exhibits degraded steady-state performance in the sense of residual errors.Recent developments have produced a new class of continuous controllers that can implicitly learn suchdisturbances through a nonlinear differential equation. This advancement opens new possibilities to refocusthe nonlinear systems community on the dual stability and optimality problem for general systems. Efforts inthis project seek to explore how such implicit learning controllers (and potential permutations) can be usedto yield analytical solutions to different optimal control problems. The ability to integrate the proposed classof implicit learning controllers (and such controllers integrated with other adaptive and learning techniques)with optimal control methods is an unexplored concept. New closed-loop error system development, stabilityanalysis, and optimal analysis methods will be required to determine the interplay of optimality, learningcapacity, and robustness. Outcomes from these aims may provide an inroad to new ways to augmentcontrollers to incorporate optimality into the design process.Broad Impact: The theoretical discoveries are expected to have a transformative impact on optimal controlmethods for uncertain nonlinear systems. One approach to solve current optimal control problems is touse numerical methods that only provide local optimal results (at best), typically do not have a proof ofstability or optimality, and are typically open-loop. Also, numerical methods are black box approaches, sothe designer is shielded from any intuition regarding the effect of the system parameters on the optimality.These issues motivate the need for analytical methods. Yet, the challenge to develop analytical solutionsis that they often do not optimize the real engineering problem because of the narrow class of systemsthat can be analytically examined. The expected outcomes of this project are new mathematical tools todevelop analytical stability and optimality solutions for broad classes of nonlinear systems. Further broadimpact will be realized by integrating the research outcomes into educational and outreach efforts. Effortswill seek to disseminate the research outcomes to engineers in industry, researchers, and students rangingfrom grade school through graduate school with an emphasis on under-represented groups. Outcomes ofthe research will be disseminated to these groups through outlets including: peer-reviewed publications,conference workshops, curriculum development, the development of a new certificate program for industrialcontrol engineers, undergraduate honor?s thesis research, existing University of Florida programs for highschooland under-represented students, and a robotics summer camp for grade school children.A-

摘要项目摘要：本项目的重点是综合新的隐式学习为基础的方法，可以最佳地实现一些控制目标的不确定非线性系统。主要研究目标包括隐式学习和自适应方法的开发和实验验证，这些方法使不确定非线性系统的期望和实际响应之间的失配收敛，同时优化性能和控制能量之间的权衡。将努力研究不同的学习和自适应方法是否具有产生更优解决方案或提高稳定性的特性。由于求解Hamilton-Jacobi方程的困难，以及缺乏用连续控制器对一般扰动进行渐近补偿的数学工具，这一研究课题的进展一直受到阻碍。随着新的隐式学习方法和一般的李雅普诺夫分析技术的出现，社会现在很好地集中越来越多的注意力，同时succeingoptimality和稳定性的不确定非线性系统。开发的控制器的学习能力将使分析最优控制解决方案的更广泛的一类工程系统比目前可能的。优化控制系统的性能沿着所需的控制努力将yielimproved的效率，可以导致及时的经济和环境costs.Intellectual优点：存在几个数学工具来合成控制器的非线性系统模型的不确定性和未建模的干扰。现有的几个工具，无论是发达国家的控制器requiresdiscontinuous反馈或表现出退化的稳态性能的残余误差的意义上，最近的发展已经产生了一类新的连续控制器，可以隐式学习suchdisturbances通过一个非线性微分方程。这一进展开辟了新的可能性refocusthe非线性系统社区的对偶稳定性和一般系统的最优性问题。在这个项目中的努力寻求探索如何使用这种隐式学习控制器（和潜在的排列）来产生不同的最优控制问题的解析解。将隐式学习控制器（以及与其他自适应和学习技术相结合的控制器）与最优控制方法相结合的能力是一个未开发的概念。新的闭环误差系统的发展，稳定性分析，和最佳分析方法将需要确定的相互作用的最佳性，learningcapacity，和鲁棒性。从这些目标的结果可能会提供一个inroad到augmentcontrollers的新方法，将最优性的设计过程中。广泛的影响：理论上的发现，预计将有一个transformative的影响不确定非线性系统的最优控制方法。解决当前最优控制问题的一种方法是使用数值方法，这些方法只能提供局部最优结果（充其量），通常没有稳定性或最优性的证明，并且通常是开环的。另外，数值方法是黑箱方法，因此设计者无法直观地了解系统参数对最优性的影响，这些问题激发了分析方法的需求。然而，开发分析解决方案的挑战在于，由于可以分析检查的系统类别很窄，因此它们通常不会优化真实的工程问题。该项目的预期成果是新的数学工具，为广泛的非线性系统开发分析稳定性和最优性解决方案。通过将研究成果纳入教育和外联工作，将产生更广泛的影响。努力将寻求传播的研究成果，以工程师在行业，研究人员和学生从小学到研究生院，重点是代表性不足的群体。研究成果将通过以下渠道传播给这些群体：同行评议的出版物、会议研讨会、课程开发、工业控制工程师新证书项目的开发、本科生荣誉？的论文研究，佛罗里达大学现有的高中和代表性不足的学生项目，以及小学生的机器人夏令营。