Optimal Transport Over a Linear Dynamical System

@article{Chen2017OptimalTO,
  title={Optimal Transport Over a Linear Dynamical System},
  author={Yongxin Chen and Tryphon T. Georgiou and Michele Pavon},
  journal={IEEE Transactions on Automatic Control},
  year={2017},
  volume={62},
  pages={2137-2152}
}
  • Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
  • Published 2017
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
  • We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ( $\dot{x}(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state… CONTINUE READING

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