Optimal Control for

OF THE DISSERTATION Optimal Control for Biological Movement Systems by Weiwei Li Doctor of Philosophy in Engineering Sciences (Aerospace Engineering) University of California, San Diego, 2006 Professor Emanuel Todorov, Chair Professor Robert E. Skelton, Co-Chair Optimal control model of biological movement provides a natural starting point for describing observed everyday behavior, and is so far the most successful model in motor control. However, in their present form, such models have a serious limitation—they rely on Linear-Quadratic-Gaussian formalism, while in reality biomechanical systems are strongly non-linear, the disturbances are control-dependent, muscle activations are nonnegative, and performance criteria are rarely quadratic. In order to handle such complex problems, we develop an iterative Linear-Quadratic-Gaussian method for locally-optimal control and estimation of nonlinear stochastic systems subject to control constraints. The new method constructs an affine feedback control law, obtained by minimizing a novel quadratic approximation to the optimal cost-to-go function. It also constructs a modified extended Kalman filter corresponding to the control law. The control law and filter are iteratively improved until convergence. Finally, the performance of the algorithm is illustrated in the context of reaching movements on a realistic human arm model. The second focus of this thesis is on the integration of optimality principles with hierarchical control scheme. We present a general approach to designing feedback control