Hierarchical approximations to optimal control

提案编号：0702221提案标题：最优控制的分层近似PI姓名： Todorov，EmanuelPI机构：加州大学圣地亚哥分校本研究的目的是发展新的算法，为近似最优控制的复杂动态系统。这种方法结合了神经科学的灵感和控制理论中的数学进步。这些算法有一个层次结构，让人想起大脑产生复杂行为的方式。较低的层次结构增强了身体，使其更容易控制。更高一级监测进展情况，并指导系统实现共同任务。通过这种方式，由于身体的复杂性与由于任务的复杂性分开了。第一类代表了随机最优控制理论的一个重大进展。一个一般的家庭的问题被确定的fundamentalequations特征的最优解原来是线性的，即使控制系统是非线性的。第二类algorithmsrepresent攻击高维非线性问题，特别是那些出现在biomechanics.broader影响提出的理论发展代表的基础工作，这是可能有持久的影响的实用框架。所提出的数值算法有可能扩展实际可解的最优控制问题的范围。最佳控制在许多科学和工程领域都引起了人们的兴趣，包括通过脑机接口恢复运动功能。教育活动包括指导研究生由本提案资助，以及在神经科学和工程接口的研究生和本科生课程的设计和教学。

Proposal Number: 0702221Proposal Title: Hierarchical approximations to optimal controlPI Name: Todorov, EmanuelPI Institution: University of California-San Diego The objective of this research is develop new algorithms forapproximately-optimal control of complex dynamical systems. The approachcombines inspiration from neuroscience with mathematical advances in controltheory. The algorithms have a hierarchical structure reminiscent of the waythe brain generates complex behavior. The lower level of the hierarchyaugments the body and makes it easier to control. The higher level monitorsprogress and steers the system towards achievement of the common task. Inthis way the complexities due to the body are separated from those due tothe task.Intellectual meritThe project includes two complementary classes of algorithms. The firstclass represents a significant advance in the theory of stochastic optimalcontrol. A general family of problems are identified where the fundamentalequations characterizing the optimal solution turn out to be linear, eventhough the controlled system is nonlinear. The second class of algorithmsrepresents a practical framework for attacking high-dimensional nonlinearproblems, particularly those that arise in biomechanics.Broader impactsThe proposed theoretical developments represent foundational work which islikely to have a lasting impact. The proposed numerical algorithms have thepotential to extend the range of practically-solvable optimal controlproblems. Optimal control is of interest in many fields of science andengineering, including the recovery of motor function via brain-machineinterfaces. Educational activities include mentoring of the graduatestudents funded by this proposal, as well as design and teaching of bothgraduate and undergraduate classes at the interface of Neuroscience andEngineering.