Optimal Design of Control Systems Stochastic and Deterministic Problems

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Deterministic and Stochastic Optimal Control

We have taken a practical path for solving this question. These are summarized on the following slide:. A tunable parameter could be a regression parameter, or variables that determine the planning horizon, number of stages and number of scenarios. In the equations above, we use tildes on variables that describe the lookahead model to avoid confusing them with the base model. This is only an issue when we are using lookahead policies. It is important to recognize that even for the same problem, each of the four classes of policies may work best, depending on the data.

We demonstrate this in the context of a simple energy storage problem. We created five problems, which we solved using each of the four classes of policies, plus a hybrid. In the graph below, we report the performance of each policy as a fraction of the posterior optimal the best you could do with perfect information. Each policy works best on one of the five problems.

Powell, S. We prefer the approach universally used in deterministic optimization where we formulate the problem first, and then we design methods to find a solution in the form of a policy. But this requires accepting that in sequential problems, we are not looking for decisions as we do in deterministic models , but rather functions or policies.

Classical strategies in stochastic optimization which are described using familiar labels such as dynamic programming, stochastic programming, robust optimization and optimal control actually represent particular classes of policies.

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So, to solve a problem using one of these approaches means you are actually choosing the class of policy before you have even started modeling the problem. Operational Research. This is my latest attempt to pull this field together in a 25 page tutorial.

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Modeling and Simulation

I teach this material in an undergraduate course at Princeton: Sequential Decision Analytics and Modeling. There is an online textbook for the course at Sequential Decision Analytics and Modeling course notes. Cite this reference as: Warren B. Most of these have been used in an undergraduate course at Princeton.

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I will make the problem sets available soon. This book is used in a graduate course on stochastic optimization. A very short presentation illustrating the jungle of stochastic optimization updated April 12, The last slide shows the evolution of seven major communities from their origin using one of the four classes of policies, to where they stand now using two, three or often all four classes of policies.

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This is a 20 minute talk on the unified framework. Click here for a list of past and pending talks. If you are interested in me giving a talk at your school or company, email me at wbpowell gmail. Some key points State variables — We claim that all properly modeled dynamic systems are Markovian, and provide a teachable, implementable definition that students can use to guide their efforts to model these systems see chapter 9 in Stochastic Optimization and Learning.

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Optimal Design of Control Systems

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