Efficient algorithms for autonomous agents facing uncertainty

© 2019 Dr Daniel Devishtan SelvaratnamThis thesis considers the design and mathematical analysis of algorithms enabling autonomous agents to operate reliably in the presence of uncertainty. The algorithms are designed to preserve computational tractability, and to respect communication constraints. Four specific problems are addressed. First, the localisation of a signal source using only random binary measurements. A Bayesian estimation procedure is adopted that discretises the search space to achieve tractability. The effect of this discretisation on convergence is analysed rigorously, as well as the effect of relying on an inexact measurement model. Measurement locations are also optimised with respect to Fisher Information. In the second, the security of general quantized Bayesian estimators is analysed from the perspective of an adversary that sends false measurements to induce a misleading posterior. Fundamental limits on the set of posteriors that can be induced are derived, along with strategies to induce them. The third problem considers the design of control laws for maintaining reliable communication links between agents as they traverse the environment. Robustness to disturbances is established theoretically. Finally, optimisation problems are tackled involving cost functions and constraints that change unpredictably as new information becomes available. Performance bounds are provided for different classes of cost functions, and both first-order and gradient free methods are examined