Optimal steering for non-Markovian Gaussian processes
Abstract
At present, the problem to steer a non-Markovian process with minimum energy between specified end-point marginal distributions remains unsolved. Herein, we consider the special case for a non-Markovian process y(t) which, however, assumes a finite-dimensional stochastic realization with a Markov state process that is fully observable. In this setting, and over a finite time horizon [0,T], we determine an optimal (least) finite-energy control law that steers the stochastic system to a final distribution that is compatible with a specified distribution for the terminal output process y(T); the solution is given in closed-form. This work provides a key step towards the important problem to steer a stochastic system based on partial observations of the state (i.e., an output process) corrupted by noise, which will be the subject of forthcoming work.
Cite
@article{arxiv.1903.00525,
title = {Optimal steering for non-Markovian Gaussian processes},
author = {Daniele Alpago and Yongxin Chen and Tryphon Georgiou and Michele Pavon},
journal= {arXiv preprint arXiv:1903.00525},
year = {2019}
}
Comments
5 pages, 2 figures