Title:
DATA PROCESSING DEVICE, CONTROL SYSTEM, DATA PROCESSING METHOD, AND PROGRAM
Document Type and Number:
WIPO Patent Application WO/2023/033132
Kind Code:
A1
Abstract:
This data processing device 1 estimates extrema [formula 140] G(∞) in [formula 144] t=∞ for a controllability grammian [formula 138] G(t) defined by [formula 2] (BB) when [formula 1] (AA) is established, where [formula 142] X(t) is an n-dimensional vector representing the state of an item being controlled, [formula 139] u(t) is an m-dimensional vector representing a control input, A is an unknown n×n matrix, and B is a known nXm matrix, the data processing device comprising: a data acquisition unit 10 for acquiring a set of chronological state data [formula 5] x([t
11, t
12], x11), x([t
2
1, t
2
2], x11), etc., x([t
q
1, t
q2], xq1) in q time sections [formula 4] [t
i
1, t
i
2] (i=1, 2, etc., q) when [formula 39] u(t)Ξ0 holds; a controllability grammian calculation unit 12 for estimating [formula 146] G(∞)=X by deriving, through numerical calculation, a solution X to a linear equation [formula 6] (CC) in relation to [formula 157] E(t):=[x(t+t
11, t
11, x
11)x(t+t
2
1, t
2
1, x
2
1), etc., x(t+t
n
1, t
n
1, x
n
1)] and [formula 158] E
0:=[x
11
x
21, etc.,
x
n
1)]; and an output unit 15 for outputting an input matrix when the controllability grammian is maximum, on the basis of an estimated maximization condition.
Inventors:
AZUMA SHUN-ICHI (JP)
BANNO IKUMI (JP)
IMURA JUN-ICHI (JP)
BANNO IKUMI (JP)
IMURA JUN-ICHI (JP)
Application Number:
PCT/JP2022/033059
Publication Date:
March 09, 2023
Filing Date:
September 02, 2022
Export Citation:
Assignee:
JAPAN SCIENCE & TECH AGENCY (JP)
International Classes:
G06F17/10
Foreign References:
| JPH0499939A | 1992-03-31 |
Other References:
ICHIRO JIKUYA, ICHIJO HODAKA: "A Note on Kalman Canonical Decomposition of Linear Periodic Continuous-time Systems - Decomposition of State Space into Controllable and Uncontrollable Parts with the Same Period of Systems -", TRANSACTIONS OF THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS, KEISOKU JIDO SEIGYO GAKKAI, TOKYO, JP, vol. 43, no. 10, 31 October 2007 (2007-10-31), JP , pages 892 - 900, XP009544131, ISSN: 0453-4654, DOI: 10.9746/ve.sicetr1965.43.892
F. PASQUALETTIS. ZAMPIERIF. BULLO: "Controllability metrics, limitations and algorithms for complex networks", IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, vol. 1, no. 1, 2014, pages 40 - 52
V. TZOUMASM.A. RAHIMIANG.J. PAPPASA. JADBABAIE: "Minimal actuator placement with bounds on control effort", IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, vol. 3, no. 1, 2016, pages 40 - 52, XP011603326, DOI: 10.1109/TCNS.2015.2444031
K. KASHIMA: "Noise response data reveal novel controllability Gramian for nonlinear network dynamics", SCIENTIFIC REPORTS, vol. 6, 2016
V.M. PRECIADOM.A. RAHIMIAN: "Controllability Gramian spectra of random networks", AMERICAN CONTROL CONFERENCE, 2016, pages 3874 - 3879
X. CHENGJ.M.A. SCHERPEN: "A new controllability Gramian for semistable systems and its application to approximation of directed networks", 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL, 2017, pages 3823 - 3828, XP033304386, DOI: 10.1109/CDC.2017.8264221
S. ZHAOF. PASQUALETTI: "Networks with diagonal controllability Gramians: analysis, graphical conditions, and design algorithms", AUTOMATICA, vol. 102, 2019, pages 10 - 18
Z. WANGD. LIU: "Data-based controllability and observability analysis of linear discrete-time systems", IEEE TRANSACTIONS ON NEURAL NETWORKS, vol. 22, no. 12, 2011, pages 2388 - 2392
D. BHATTACHARJEEB. KLOSEG.B. JACOBSM.S. HEMATI: "Data-driven selection of actuators for optimal control of airfoil separation", THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, vol. 34, no. 4, 2020, pages 557 - 575
K. ZHOUJ.C. DOYLEK. GLOVER: "Robust and Optimal Control", 1996, PRENTICE HALL
C. KENNEYG. HEWER: "Trace norm bounds for stable Lyapunov operators", LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 221, 1995, pages 1 - 18
F. PASQUALETTIS. ZAMPIERIF. BULLO: "Controllability metrics, limitations and algorithms for complex networks", IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, vol. 1, no. 1, 2014, pages 40 - 52
V. TZOUMASM.A. RAHIMIANG.J. PAPPASA. JADBABAIE: "Minimal actuator placement with bounds on control effort", IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, vol. 3, no. 1, 2016, pages 40 - 52, XP011603326, DOI: 10.1109/TCNS.2015.2444031
K. KASHIMA: "Noise response data reveal novel controllability Gramian for nonlinear network dynamics", SCIENTIFIC REPORTS, vol. 6, 2016
V.M. PRECIADOM.A. RAHIMIAN: "Controllability Gramian spectra of random networks", AMERICAN CONTROL CONFERENCE, 2016, pages 3874 - 3879
X. CHENGJ.M.A. SCHERPEN: "A new controllability Gramian for semistable systems and its application to approximation of directed networks", 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL, 2017, pages 3823 - 3828, XP033304386, DOI: 10.1109/CDC.2017.8264221
S. ZHAOF. PASQUALETTI: "Networks with diagonal controllability Gramians: analysis, graphical conditions, and design algorithms", AUTOMATICA, vol. 102, 2019, pages 10 - 18
Z. WANGD. LIU: "Data-based controllability and observability analysis of linear discrete-time systems", IEEE TRANSACTIONS ON NEURAL NETWORKS, vol. 22, no. 12, 2011, pages 2388 - 2392
D. BHATTACHARJEEB. KLOSEG.B. JACOBSM.S. HEMATI: "Data-driven selection of actuators for optimal control of airfoil separation", THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, vol. 34, no. 4, 2020, pages 557 - 575
K. ZHOUJ.C. DOYLEK. GLOVER: "Robust and Optimal Control", 1996, PRENTICE HALL
C. KENNEYG. HEWER: "Trace norm bounds for stable Lyapunov operators", LINEAR ALGEBRA AND ITS APPLICATIONS, vol. 221, 1995, pages 1 - 18
Attorney, Agent or Firm:
MORISHITA Sakaki (JP)
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