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Trajectory control and interconnection of 1D and nD systems

Trajectory control and interconnection of 1D and nD systems
Trajectory control and interconnection of 1D and nD systems
In this paper we examine the relationship between control viewed as concatenation of trajectories, and control viewed as interconnection of systems. We show that, for 1D linear time-invariant systems, the ability to obtain a given subsystem by regular interconnection (a prerequisite for any feedback-type structure) is equivalent to the ability to drive any trajectory into that subsystem. However in the case of multidimensional (nD) systems the former is a stronger property than the latter. Trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space, by introducing latent or auxiliary variables. This leads as a by-product to the notion of controlling a system by means of latent variables.
107-34
Rocha, P.
7fb9de01-75f9-4cb8-96a2-dbbb8cdf28f4
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rocha, P.
7fb9de01-75f9-4cb8-96a2-dbbb8cdf28f4
Wood, J.
65587872-7126-469a-851a-d60195d39058

Rocha, P. and Wood, J. (2001) Trajectory control and interconnection of 1D and nD systems. SIAM Journal of Control and Optimization, 40 (1), 107-34.

Record type: Article

Abstract

In this paper we examine the relationship between control viewed as concatenation of trajectories, and control viewed as interconnection of systems. We show that, for 1D linear time-invariant systems, the ability to obtain a given subsystem by regular interconnection (a prerequisite for any feedback-type structure) is equivalent to the ability to drive any trajectory into that subsystem. However in the case of multidimensional (nD) systems the former is a stronger property than the latter. Trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space, by introducing latent or auxiliary variables. This leads as a by-product to the notion of controlling a system by means of latent variables.

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More information

Published date: 2001
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 256191
URI: http://eprints.soton.ac.uk/id/eprint/256191
PURE UUID: dd0f56f8-2196-47fd-b0b0-048b4c7b5231

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Date deposited: 21 Dec 2001
Last modified: 10 Dec 2021 20:42

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Contributors

Author: P. Rocha
Author: J. Wood

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