Biologically Inspired Algorithms for Optimal Control

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In the past few years, efforts to codify the organizing principles behind biological systems have been capturing the attention of a growing number of researchers in the systems and control community. This endeavor becomes increasingly important as new technologies make it possible to engineer complex cooperating systems that are nevertheless faced with many of the challenges long-overcome by their natural counterparts. One area in particular where biology serves as an inspiring but still distant example, involves systems in which members of a species cooperate to form collectives whose abilities are beyond those of individuals. This paper looks to the process by which ants optimize their foraging trails as inspiration for an organizing principle by which groups of dynamical systems can solve a class of optimal control problems. We explore the use of a strategy termed `local pursuit', which allows members of the group to overcome their limitations with respect to sensing range and available information through the use of neighbor-to-neighbor interactions. Local pursuit enables the group to find an optimal solution by iteratively improving upon an initial feasible control. We show that our proposed strategy subsumes previous pursuit-based models for ant-trail optimization and applies to a large array of problems, including many of the classical situations in optimal control. The performance of our algorithm is illustrated in a series of numerical experiments. Ongoing work directions related to local pursuit are also discussed in this document.