### Abstract

We consider a control system with "nonclassical" dynamics: ẋ = f(t, x, u, D_{x}u), where the right hand side depends also on the first order partial derivatives of the feedback control function. Given a probability distribution on the initial data, we seek a feedback u = u(t, x) which minimizes the expected value of a cost functional. Various relaxed formulations of this problem are introduced. In particular, three specific examples are studied, showing the equivalence or non-equivalence of these approximations.

Original language | English (US) |
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Pages (from-to) | 249-271 |

Number of pages | 23 |

Journal | Nonlinear Differential Equations and Applications |

Volume | 20 |

Issue number | 2 |

DOIs | |

State | Published - May 3 2013 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

Bressan, A., & Wei, D. (2013). Examples of nonclassical feedback control problems.

*Nonlinear Differential Equations and Applications*,*20*(2), 249-271. https://doi.org/10.1007/s00030-012-0165-2