Advanced

Model-Free Plant Tuning

Blanchini, F.; Fenu, G.; Giordano, Giulia LU and Pellegrino, F. A. (2017) In IEEE Transactions on Automatic Control 62(6). p.2623-2634
Abstract
Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, this paper considers the problem of tuning (i.e., driving to a desired value) the output, by suitably choosing the input. It is shown that, if the polytope is robustly non-singular (or has full rank, in the non-square case), then a suitable tuning scheme drives the output to the desired point. The proof exploits a Lyapunov-like function and applies a well known game-theoretic result, concerning the existence of a saddle point for a minmax zero-sum game. When the plant output is represented in an implicit form, it is shown that the same result can be obtained,... (More)
Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, this paper considers the problem of tuning (i.e., driving to a desired value) the output, by suitably choosing the input. It is shown that, if the polytope is robustly non-singular (or has full rank, in the non-square case), then a suitable tuning scheme drives the output to the desired point. The proof exploits a Lyapunov-like function and applies a well known game-theoretic result, concerning the existence of a saddle point for a minmax zero-sum game. When the plant output is represented in an implicit form, it is shown that the same result can be obtained, resorting to a different Lyapunov-like function. The case in which proper input or output constraints must be enforced during the transient is considered as well. Some application examples are proposed to show the effectiveness of the approach. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Games, Generators, Jacobian matrices, Robustness, Steady-state, Transient analysis, Tuning
in
IEEE Transactions on Automatic Control
volume
62
issue
6
pages
12 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85026770510
  • wos:000402733600002
ISSN
0018-9286
DOI
10.1109/TAC.2016.2616025
language
English
LU publication?
yes
id
d60eb6a7-2fdf-49e3-a1a3-e2f53c285795
date added to LUP
2016-11-26 14:55:30
date last changed
2018-10-03 11:37:03
@article{d60eb6a7-2fdf-49e3-a1a3-e2f53c285795,
  abstract     = {Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, this paper considers the problem of tuning (i.e., driving to a desired value) the output, by suitably choosing the input. It is shown that, if the polytope is robustly non-singular (or has full rank, in the non-square case), then a suitable tuning scheme drives the output to the desired point. The proof exploits a Lyapunov-like function and applies a well known game-theoretic result, concerning the existence of a saddle point for a minmax zero-sum game. When the plant output is represented in an implicit form, it is shown that the same result can be obtained, resorting to a different Lyapunov-like function. The case in which proper input or output constraints must be enforced during the transient is considered as well. Some application examples are proposed to show the effectiveness of the approach.},
  author       = {Blanchini, F. and Fenu, G. and Giordano, Giulia and Pellegrino, F. A.},
  issn         = {0018-9286},
  keyword      = {Games,Generators,Jacobian matrices,Robustness,Steady-state,Transient analysis,Tuning},
  language     = {eng},
  number       = {6},
  pages        = {2623--2634},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Model-Free Plant Tuning},
  url          = {http://dx.doi.org/10.1109/TAC.2016.2616025},
  volume       = {62},
  year         = {2017},
}