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Optimal control for biological movement systems

Abstract

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 hierarchies for redundant biomechanical systems, that approximate the (non-hierarchical) optimal control law but have much lower computational demands. This hierarchy has two levels of feedback control: the high level is designed as an optimal feedback controller operating on a simplified plant; the low level is responsible for transforming the dynamics of the true plant into the desired virtual dynamics. The new method will be useful not only for modelling neural control of movement, but also for designing Functional Electric Stimulation systems that have to achieve task goals by activating muscles in real time. Another contribution of this thesis is to present an estimation design method for multiplicative noise system using linear matrix inequalities (LMIs) approach. Sufficient conditions for the existence of the state estimator are provided; these conditions are expressed in terms of LMIs and the parametrization of all admissible solutions is provided. We show that a mild additional constraint for scaling will make the problem convex

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