Spatially distributed systems such as reactor networks hosting multiple autocatalytic species demonstrate a rich spectrum of complex behavior. From a control systems perspective, spatially distributed systems offer a difficult control challenge because of their distributed nature, nonlinearity, and high order. Furthermore, manipulation of the network states may require simultaneous control actions in different parts of the system and may need transients through several operating regimes to achieve the desired operation. The lack of accurate and computationally efficient model-based techniques for large, spatially distributed systems results in complications in controlling the system, either in disturbance rejection or changing the operational regimes of the system. A hierarchical, agent-based control structure is presented whereby local control objectives may be changed in order to achieve the global control objective. The performance of the control system is demonstrated for several global objectives. The challenge posed is to control the spatial distribution of autocatalytic species in a network of five reactors hosting two species using the interaction flow rates as the manipulated variables. The multi-agent control system is able to effectively explore the parameter space of the network and intelligently manipulate the network flow rates such that the desired spatial distribution of species is achieved.