Hierarchical approximations to optimal control

提案编号：0702221提案标题：最优控制的分层近似PI名称：托多罗夫，伊曼纽尔PI研究所：加州大学圣地亚哥分校这项研究的目的是为复杂动态系统的近似最优控制开发新的算法。这种方法将神经科学的灵感与控制理论中的数学进步结合在一起。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。层次结构的较低级别扩大了主体，使其更容易控制。较高级别监测进展并引导系统朝着完成共同任务的方向发展。通过这种方式，身体引起的复杂性与任务引起的复杂性被分开。智力优点该项目包括两个互补的算法类别。第一类代表了随机最优控制理论的重大进步。确定了一类一般的问题，其中表征最优解的基本方程被证明是线性的，即使受控系统是非线性的。第二类算法代表了一个解决高维非线性问题的实用框架，特别是那些在生物力学中出现的问题。所提出的数值算法有可能扩大实际可解的最优控制问题的范围。最优控制在许多科学和工程领域都很有意义，包括通过脑机接口恢复运动功能。教育活动包括指导这项提议资助的毕业生，以及设计和教授神经科学和工程学的研究生和本科生课程。

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.