Orthogonal polynomial bases for data-driven analysis and control of continuous-time systems
Orthogonal polynomial bases for data-driven analysis and control of continuous-time systems
We use polynomial approximation theory to perform data-driven analysis and control of linear, continuous-time invariant systems. We transform the continuous-time input- and state trajectories into discrete sequences consisting of the coefficients of their orthog- onal polynomial bases representations. We show that the dynamics of the transformed input- and state signals and those of the original continuous-time trajectories are de- scribed by the same system matrices. We investigate informativity, quadratic stabilization, and H2-performance problems for continuous-time systems. We deal with the case in which machine-precision accuracy in the representation of continuous-time signals can be achieved from the data using a finite number of basis elements, and the case in which the approximation error is non-negligible.
Continuous-time linear systems, H2-performance, data-driven control, informativity, polynomial orthogonal basis, quadratic stabilization, <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math> </inline-formula>-performance, System dynamics, Transforms, Standards, Chebyshev approximation, Approximation error, Controllability, Trajectory
1-12
Rapisarda, P.
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
van Waarde, H.J.
906bc83a-bd1a-4cd3-8a4a-af7d7e8e7ef7
Camlibel, M.K.
de670aa3-6a3e-4a7b-8a78-0b58189080ab
Rapisarda, P.
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
van Waarde, H.J.
906bc83a-bd1a-4cd3-8a4a-af7d7e8e7ef7
Camlibel, M.K.
de670aa3-6a3e-4a7b-8a78-0b58189080ab
Rapisarda, P., van Waarde, H.J. and Camlibel, M.K.
(2023)
Orthogonal polynomial bases for data-driven analysis and control of continuous-time systems.
IEEE Transactions on Automatic Control, .
(doi:10.1109/TAC.2023.3321214).
Abstract
We use polynomial approximation theory to perform data-driven analysis and control of linear, continuous-time invariant systems. We transform the continuous-time input- and state trajectories into discrete sequences consisting of the coefficients of their orthog- onal polynomial bases representations. We show that the dynamics of the transformed input- and state signals and those of the original continuous-time trajectories are de- scribed by the same system matrices. We investigate informativity, quadratic stabilization, and H2-performance problems for continuous-time systems. We deal with the case in which machine-precision accuracy in the representation of continuous-time signals can be achieved from the data using a finite number of basis elements, and the case in which the approximation error is non-negligible.
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Accepted/In Press date: 2023
e-pub ahead of print date: 2 October 2023
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IEEE
Keywords:
Continuous-time linear systems, H2-performance, data-driven control, informativity, polynomial orthogonal basis, quadratic stabilization, <inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math> </inline-formula>-performance, System dynamics, Transforms, Standards, Chebyshev approximation, Approximation error, Controllability, Trajectory
Identifiers
Local EPrints ID: 482993
URI: http://eprints.soton.ac.uk/id/eprint/482993
ISSN: 0018-9286
PURE UUID: c4425576-1e2d-4c40-999f-d75005f51a88
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Date deposited: 18 Oct 2023 16:42
Last modified: 17 Mar 2024 04:52
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Contributors
Author:
P. Rapisarda
Author:
H.J. van Waarde
Author:
M.K. Camlibel
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