In Part I of this tutorial, we provided a canonical modeling framework for sequential, stochastic optimization (control) problems. A major feature of this framework is a clear separation of the process of modeling a problem, versus the design of policies to solve the problem. In Part II, we provide additional discussion behind some of the more subtle concepts such as the construction of a state variable. We illustrate the modeling process using an energy storage problem. We then create five variations of this problem designed to bring out the features of the different policies. The first four of these problems demonstrate that each of the four classes of policies is best for particular problem characteristics. The fifth policy is a hybrid that illustrates the ability to combine the strengths of multiple policy classes.
There is a wide range of problems in energy systems that require making decisions in the presence of different forms of uncertainty. The fields that address sequential, stochastic decision problems lack a standard canonical modeling framework, with fragmented, competing solution strategies. Recognizing that we will never agree on a single notational system, this two-part tutorial proposes a simple, straightforward canonical model (that is most familiar to people with a control theory background), and introduces four fundamental classes of policies which integrate the competing strategies that have been proposed under names such as control theory, dynamic programming, stochastic programming and robust optimization. Part II of the tutorial illustrates the modeling framework using a simple energy storage problem, where we show that, depending on the problem characteristics, each of the four classes of policies may be best. where he has taught since 1981. His research specializes in computational stochastic optimization, with applications in energy, transportation, health, and finance. He has authored/coauthored over 200 publications and two books. He founded and directs CASTLE Labs (http://www.castlelab.princeton.edu), specializing in fundamental contributions to computational stochastic optimization with a wide range of applications.
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