## Abstract

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be expressed as a, possibly infinite, system of deterministic linear ordinary differential equations. By casting the problem as a deterministic control problem in moment space, semidefinite programming is used to find a lower bound on the optimal solution. The constraints in the semidefinite program are imposed by the ordinary differential equations for moment dynamics and semidefiniteness of the outer product of moments. From the solution to the semidefinite program, an approximate optimal control strategy can be constructed using a least squares method. In the linear quadratic case, the method gives an exact solution to the optimal control problem. In more complex problems, an infinite number of moment differential equations would be required to compute the optimal control law. In this case, we give a procedure to increase the size of the semidefinite program, leading to increasingly accurate approximations to the true optimal control strategy.

Original language | English (US) |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1990-1995 |

Number of pages | 6 |

ISBN (Electronic) | 9781509018376 |

DOIs | |

State | Published - Dec 27 2016 |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016 |

### Publication series

Name | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |
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### Other

Other | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Country/Territory | United States |

City | Las Vegas |

Period | 12/12/16 → 12/14/16 |

### Bibliographical note

Publisher Copyright:© 2016 IEEE.