Feedback control and the arrow of time

Abstract

The purpose of this article is to highlight the central role that the time asymmetry of stability plays in feedback control. We show that this provides a new perspective on the use of doubly-infinite or semi-infinite time-axes for signal spaces in control theory. We then focus on the implication of this time asymmetry in modelling uncertainty, regulation and robust control. We point out that modelling uncertainty and the ease of control depend critically on the direction of time. We also discuss the relationship of this control-based time-arrow with the well-known arrows of time in physics.

Keywords:

• stability
• feedback control
• thermodynamics
• time-asymmetry
• robust control
• reversibility

Acknowledgements

We are grateful to Jan Willems for helpful comments on an earlier draft. The authors would like to thank the anonymous reviewers for their comments. This work was partially supported by the NSF and AFOSR.