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arXiv · 1903.00525

Optimal steering for non-Markovian Gaussian processes

Daniele Alpago·Yongxin Chen·Tryphon Georgiou·Michele Pavon
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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.

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Daniele Alpago, Yongxin Chen, Tryphon Georgiou, Michele Pavon. 2019-03-01. Optimal steering for non-Markovian Gaussian processes. https://arxiv.org/abs/1903.00525

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