Biologically-inspired optimal control

Abstract

Inspired by the collective activities of ant colonies, and by their ability to gradually optimize their foraging trails, this dissertation investigates the cooperative solution of a broad class of trajectory optimization problems with various types of boundary conditions. A set of cooperative control algorithms are presented and proved to converge to an optimal solution by iteratively optimizing an initially feasible trajectory/control pair. The proposed algorithms organize a group of identical control systems by imposing a type of pair-wise interaction known as "local pursuit". The bio-inspired approach taken here requires only short-range, limited interactions between group members, avoids the need for a "global map" of the environment in which the group evolves, and solves an optimal control problem in "small" pieces, in a manner which is made precise. These features enable the application of the proposed algorithms in numerical optimization, leading to an increase of the permitting size of problems that can be solved, as well as a decrease of numerical errors incurred in ill-conditioned problems. The algorithms' effectiveness is illustrated in a series of simulations and laboratory experiments