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Linear Programming Approach to Singularly Perturbed Problems of Optimal

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Problems of optimal control (POC) of dynamical systems arise in a variety of applications and remain in the focus of attention of many researchers. Common theoretical tools for analysis and solution of POC are Pontryagin’s maximum principle and Hamilton-Jacobi-Bellman equations. In this presentation, we will discuss a much less conventional approach to POC based on the fact that, under certain conditions, the latter can be “equivalently” reformulated as infinite-dimensional linear programming problems. The main attention will be paid to an LP based analysis and solution of so-called singularly perturbed POC , in which the state variables change their values with rates of different order of magnitude (so that some of them can be considered to be fast/slow with respect to others). Theoretical developments will be illustrated with numerical examples..

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