Stylized Models to Analyze Robustness of Irrigation Systems

Irrigation systems are a prevalent feature in human history. They are archetypal examples of human efforts to control spatial and temporal environmental heterogeneity. In this chapter, we report on some preliminary results to understand the emergence, robustness, and collapse of irrigation systems, using a suite of stylized models. As a starting point, we perceive irrigation systems as similar to control systems in engineering. The “irrigation society” may usefully be thought of as a controller engineered to meet specific performance criteria defined by sustained, relatively constant food output, given both spatially and temporally variable water input. That is, the well-functioning irrigation society control system will get the right amount of water to the right place at the right time. This, of course, is a nontrivial task. Flying a large jet on autopilot is a nontrivial task as well, yet modern feedback-control systems can do this quite well. Control engineers have devised highly effective control systems that perform well under a variety of conditions. Key issues faced by feedback control designers are noisy feedback from the system (either because the system has some random components or because the system’s state cannot be perfectly known) and uncertainty about how the system actually works (model uncertainty). These conditions would certainly be characteristic of an irrigation system. How does one design a feedback (closed-loop) control system under such circumstances? This question is the subject of the field of robust control. It is in