<abstract xmlns="http://www.w3.org/1999/xhtml"><p>An information based method for solving stochastic control problems with partial observation is proposed. First, information-theoretic lower bounds of the cost function are analysed. It is shown, under rather weak assumptions, that reduction in the expected cost with closed-loop control compared with the best open-loop strategy is upper bounded by a non-decreasing function of mutual information between control variables and the state trajectory. On the basis of this result, an <italic>information based control</italic> (IBC) method is developed. The main idea of IBC consists in replacing the original control task by a sequence of control problems that are relatively easy to solve and such that information about the system state is actively generated. Two examples of the IBC operation are given. It is shown that the method is able to find an optimal solution without using dynamic programming at least in these examples. Hence the computational complexity of IBC is substantially smaller than that of dynamic programming, which is the main advantage of the proposed method.</p></abstract>

An information based method for solving stochastic control problems with partial observation is proposed. First, information-theoretic lower bounds of the cost function are analysed. It is shown, under rather weak assumptions, that reduction in the expected cost with closed-loop control compared with the best open-loop strategy is upper bounded by a non-decreasing function of mutual information between control variables and the state trajectory. On the basis of this result, an information based control (IBC) method is developed. The main idea of IBC consists in replacing the original control task by a sequence of control problems that are relatively easy to solve and such that information about the system state is actively generated. Two examples of the IBC operation are given. It is shown that the method is able to find an optimal solution without using dynamic programming at least in these examples. Hence the computational complexity of IBC is substantially smaller than that of dynamic programming, which is the main advantage of the proposed method.

An Information Based Approach to Stochastic Control Problems

Faculty of Automatic Control and Robotics

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"An Information Based Approach to Stochastic Control Problems"}

An information based method for solving stochastic control problems with partial observation is proposed. First, information-theoretic lower bounds of the cost...

An Information Based Approach to Stochastic Control Problems

Published Online: Apr 03, 2020

Page range: 23 - 34

Received: Mar 09, 2019

Accepted: Oct 31, 2019

DOI: https://doi.org/10.34768/amcs-2020-0002

Keywords
stochastic control, feedback, information, entropy

© 2020 Piotr Bania, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

An Information Based Approach to Stochastic Control Problems

Published Online: Apr 03, 2020

Page range: 23 - 34

Received: Mar 09, 2019

Accepted: Oct 31, 2019

DOI: https://doi.org/10.34768/amcs-2020-0002

Keywordsstochastic control, feedback, information, entropy

© 2020 Piotr Bania, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
stochastic control, feedback, information, entropy