Hierarchical approximations to optimal control

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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.