Averaging of Singularly Perturbed Control Systems and LP Approach to Optimal Control

This book provides a systematic exposition of averaging techniques for singularly perturbed control systems, with emphasis on their interplay with infinite-dimensional linear programming (LP) formulations of optimal control problems. The author provides a comprehensive study of averaging methods for singularly perturbed control systems, including averaging over fast control-state trajectories and over the occupational measures generated by such trajectories; establishes rigorous connections between optimal control problems with time-discounting or time-averaging criteria and infinite-dimensional linear programming problems, proves strong duality for the latter, and uses this duality to analyze and construct optimal and near-optimal controls; and develops LP-based techniques for the analysis and construction of asymptotically near-optimal controls for singularly perturbed systems and illustrates these techniques by numerical examples.