Cooperative Control of Multiple Agents and Search Strategy

This chapter discusses problems dealing with cooperative control of multiple agents moving in a region. An appropriate search strategy for the whole system can be embodied: hierarchical, coordinated, or cooperative. Geometrical and computational aspects of many-target search problems axe considered. Nonlinear and bilinear processes of search for moving objects are proposed. Search problems of ecological danger objects and detection of biological and chemical agents using multi-spectral information are also considered. Multiagent coordination problems are studied in detail. This problem is addressed for a class of targets for which control Lyapunov functions can be derived. We describe such a multiagent system by a hierarchical structure, which can be simplified using a fiber bundle. Then, using geometrical techniques, we study controllability, observability, and optimality problems. In addition, we also consider a cooperative problem when the agents motions must satisfy a separation constraint throughout the encounter to be conflict-free. A classification of maneuvers based on different commutative diagrams is introduced using their fiber bundle representation. In the case of two agents, these optimality conditions allow us to construct optimal maneuvers geometrically.