Robust Control An Entry for the New Palgrave, 2nd Edition

1. OVERVIEW Robust control considers the design of decision or control rules that fare well across a range of alternative models. Thus robust control is inherently about model uncertainty, particularly focusing on the implications of model uncertainty for decisions. Robust control originated in the 1980s in the control theory branch of the engineering and applied mathematics literature, and it is now perhaps the dominant approach in control theory. Robust control gained a foothold in economics in the late 1990s and has seen increasing numbers of economic applications in the past few years.1 The basic issues in robust control arise from adding more detail to the opening sentence above – that a decision rule performs well across alternative models. To begin, define a model as a specification of a probability distribution over outcomes of interest to the decision maker, which is influenced by a decision or control variable. Then model uncertainty simply means that the decision maker faces subjective uncertainty about the specification of this probability distribution. A first key issue in robust control then is to specify the class of alternative models which the decision maker entertains. As we discuss below, there are many approaches to doing so, with the most common cases taking a benchmark nominal model as a starting point and considering perturbations of this model. How to specify and measure the magnitude of the perturbations are key practical considerations. With the model set specified, the next issue is how to choose a decision rule and thus what it means for a rule to “perform well” across models. In Bayesian analysis, the deci-