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RESEARCH PRODUCT
Mixed integer optimal compensation: Decompositions and mean-field approximations
Tamer BasarQuanyan ZhuDario Bausosubject
Model predictive controlApproximation theoryMathematical optimizationLinear programmingBranch and priceShortest path problemDecomposition method (constraint satisfaction)Optimal controlInteger programmingMathematicsdescription
Mixed integer optimal compensation deals with optimizing integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this issue, we propose a decomposition method which turns the original n-dimensional problem into n independent scalar problems of lot sizing form. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon. This last reformulation step mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of the exogenous signal and the local state average. We discuss a large population mean-field type of approximation as well as the application of predictive control methods.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-06-01 | 2012 American Control Conference (ACC) |