Optimal Control of Active Sensing Systems

This dissertation is concerned with active sensing systems, where the mechanism for observing a dynamical system may be controlled. The main objective throughout is to formalize the objectives of active sensing as optimization problems, so that the trade-off between the costs of measurement and costs of uncertainty can be managed in a principled way. Tools from optimal control theory are then brought to bear on the design of measurement policies.;The first section considers optimization of measurement schedules for continuous-time Markov jump processes. It is shown that if each costly measurement provides complete observation of the underlying state, a deterministic feedback policy minimizes the infinite-horizon average cost. The average cost is parametrized by a finite vector of inter-observation wait times, and a gradient-based solution method is given to optimize these times. To obtain a globally-convergent solution method for a wider class of problems, the problem is recast as a semi-Markov decision process. Policy iteration is then applied to solve the example of optimizing diabetes screening protocols.;In the second section, active sensing policies for linear Gauss-Markov systems are determined by considering optimal control of the Kalman-Bucy filter variance. Necessary conditions for optimality are derived, and a gradient-based method for finding locally optimal policies for the finite-horizon problem is described. The optimality of time-invariant policies is demonstrated for the infinite-horizon attention control problem. In contrast, for data-aggregating problems, which describe sensor networks composed of nodes with internal dynamics, rhythmic oscillation in the network interconnections sometimes leads to a reduction in the estimator variance.;Finally, respiratory motion compensation for cardiac MRI is considered. The motion-adapted average is introduced and its asymptotic properties are compared to those of the conventional averaging approach. Motion-adapted averaging is applied to imaging of the coronary arteries of 14 healthy subjects and is found to significantly improve vessel sharpness in comparison with conventional averaging, and to significantly increase SNR in comparison with retrospective navigator gating. The opportunities for an active sensing approach to optimize MRI data acquisition are then described.