Information-theoretic approach to the study of control systems
| dc.creator | Touchette, Hugo | |
| dc.creator | Lloyd, Seth | |
| dc.date | 2001-04-02 | |
| dc.date | 2003-05-16 | |
| dc.date.accessioned | 2026-07-07T05:45:39Z | |
| dc.date.available | 2026-07-07T05:45:39Z | |
| dc.description | We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, takes the initial state of a system to be controlled and transforms it into a target state. In this sense, a controller can be thought of as an actuation channel that acts on inputs to produce desired outputs. In this transformation process, two different control strategies can be adopted: (i) the controller applies an actuation dynamics that is independent of the state of the system to be controlled (open-loop control); or (ii) the controller enacts an actuation dynamics that is based on some information about the state of the controlled system (closed-loop control). Using this communication channel model of control, we provide necessary and sufficient conditions for a system to be perfectly controllable and perfectly observable in terms of information and entropy. In addition, we derive a quantitative trade-off between the amount of information gathered by a closed-loop controller and its relative performance advantage over an open-loop controller in stabilizing a system. This work supplements earlier results [H. Touchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)] by providing new derivations of the advantage afforded by closed-loop control and by proposing an information-based optimality criterion for control systems. New applications of this approach pertaining to proportional controllers, and the control of chaotic maps are also presented. | |
| dc.description | 18 pages, 7 eps figures | |
| dc.identifier | https://arxiv.org/abs/physics/0104007 | |
| dc.identifier | http://arxiv.org/abs/physics/0104007 | |
| dc.identifier | Physica A 331, 140-172, 2004 | |
| dc.identifier | doi:10.1016/j.physa.2003.09.007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/84065 | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.subject | General Physics | |
| dc.subject | Quantum Physics | |
| dc.title | Information-theoretic approach to the study of control systems | |
| dc.type | text |