dorsal/arxiv
View SchemaInformation-theoretic approach to the study of control systems
| Authors | Hugo Touchette, Seth Lloyd |
|---|---|
| Categories | |
| ArXiv ID | physics/0104007 |
| URL | https://arxiv.org/abs/physics/0104007 |
| DOI | 10.1016/j.physa.2003.09.007 |
| Journal | Physica A 331, 140-172, 2004 |
Abstract
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.
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"abstract": "We propose an information-theoretic framework for analyzing control systems\nbased on the close relationship of controllers to communication channels. A\ncommunication channel takes an input state and transforms it into an output\nstate. A controller, similarly, takes the initial state of a system to be\ncontrolled and transforms it into a target state. In this sense, a controller\ncan be thought of as an actuation channel that acts on inputs to produce\ndesired outputs. In this transformation process, two different control\nstrategies can be adopted: (i) the controller applies an actuation dynamics\nthat is independent of the state of the system to be controlled (open-loop\ncontrol); or (ii) the controller enacts an actuation dynamics that is based on\nsome information about the state of the controlled system (closed-loop\ncontrol). Using this communication channel model of control, we provide\nnecessary and sufficient conditions for a system to be perfectly controllable\nand perfectly observable in terms of information and entropy. In addition, we\nderive a quantitative trade-off between the amount of information gathered by a\nclosed-loop controller and its relative performance advantage over an open-loop\ncontroller in stabilizing a system. This work supplements earlier results [H.\nTouchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)] by providing new\nderivations of the advantage afforded by closed-loop control and by proposing\nan information-based optimality criterion for control systems. New applications\nof this approach pertaining to proportional controllers, and the control of\nchaotic maps are also presented.",
"arxiv_id": "physics/0104007",
"authors": [
"Hugo Touchette",
"Seth Lloyd"
],
"categories": [
"physics.data-an",
"physics.gen-ph",
"quant-ph"
],
"doi": "10.1016/j.physa.2003.09.007",
"journal_ref": "Physica A 331, 140-172, 2004",
"title": "Information-theoretic approach to the study of control systems",
"url": "https://arxiv.org/abs/physics/0104007"
},
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