公开(公告)号：US20240403384A1

公开(公告)日：2024-12-05

申请号：US18688728

申请日：2022-09-02

Applicant: JAPAN SCIENCE AND TECHNOLOGY AGENCY

Inventor： Shun-ichi AZUMA ,  Ikumi BANNO ,  Jun-ichi IMURA

IPC: G06F17/16

Abstract: A data processing device to estimate the limit: G ⁡ ( ∞ ) [ equation ⁢ 140 ] of a controllability Gramian: G ⁡ ( t ) [ equation ⁢ 138 ] defined by: G ⁡ ( t ) : = ∫ 0 t c A ⁢ τ ⁢ BB ⊤ ⁢ e A ⊤ ⁢ τ ⁢ d ⁢ τ [ equation ⁢ 2 ] in: t = ∞ [ equation ⁢ 144 ] when: x ˙ ( t ) = Ax ⁡ ( t ) + Bu ⁡ ( t ) [ equation ⁢ 1 ] holds, where: x ⁡ ( t ) [ equation ⁢ 142 ] is an n-dimensional vector representing the state of a control object: u ⁡ ( t ) [ equation ⁢ 139 ] is an m-dimensional vector representing the control input, A is an unknown n×n matrix and B is a known n×m matrix, comprises: a data acquisition unit that acquires a set of time-series state data: x ⁡ ( [ t 11 , t 1 ⁢ 2 ] , x 1 ⁢ 1 ) , x ⁡ ( [ t 2 ⁢ 1 , t 2 ⁢ 2 ] , x 1 ⁢ 1 ) , … , x ⁡ ( [ t q ⁢ 1 , t q ⁢ 2 ] , x q ⁢ 1 ) [ equation ⁢ 5 ] for the following q time intervals: [ t i ⁢ 1 , t i ⁢ 2 ] [ equation ⁢ 4 ] ( i   = 1 , 2 , … , q ) when: u ⁡ ( t ) ≡ 0 [ equation ⁢ 39 ] holds; a controllability Gramian calculation unit that defines: [ equation ⁢ 75 ]  z ⁡ ( t ) ∈ R n expressed as: ( 13 ) z ˙ ( t ) = A ⊤ ⁢ z ⁡ ( t ) [ equation ⁢ 74 ] calculates: ( 16 ) z ⊤ ( t 2 ) ⁢ Xz ⁡ ( t 2 ) - z ⊤ ( t 1 ) ⁢ Xz ⁡ ( t 1 ) = - ∫ t 1 t 2 z ⊤ ( t ) ⁢ BB T ⁢ z ⁡ ( t ) ⁢ dt [ equation ⁢ 81 ] z ⁡ ( t + t i ⁢ 1 , t i ⁢ 1 , x i ⁢ 1 ) = ( E ⁡ ( t ) ⁢ E 0 - 1 ) ⊤ ⁢ x i ⁢ 1 [ equation ⁢ 89 ] and estimates: G ⁡ ( ∞ ) = X [ equation ⁢ 146 ] by numerically obtaining the solution X of the following linear equation: [ Equation ⁢ 6 ]  x i ⁢ 1 ⊤ ( E ⁡ ( h ) ⁢ E 0 - 1 ) ⁢ X ⁡ ( E ⁡ ( h ) ⁢ E 0 - 1 ) ⊤ ⁢ x i ⁢ 1 - x i ⁢ 1 ⊤ ⁢ Xx i ⁢ 1 = - ∫ 0 h x i ⁢ 1 ⊤ ( E ⁡ ( t ) ⁢ E 0 - 1 ) ⁢ BB ⊤ ( E ⁡ ( t ) ⁢ E 0 - 1 ) ⊤ ⁢ x i ⁢ 1 ⁢ dt ( i = 1 , 2 , … , q ) with respect to: [ equation ⁢ 157 ]  E ⁡ ( t ) := [ x ( ? + ? , ? , x 11 x ⁡ ( ? + ? , ? , x 21 ) … x ⁡ ( t + t n ⁢ 1 , t n ⁢ 1 , x n ⁢ 1 ) ] [ equation ⁢ 158 ]  E 0 := [ x 11 x 21 … x n ⁢ 1 ] ; ? indicates text missing or illegible when filed and an output unit that outputs the input matrix when the controllability Gramian is maximized based on the estimated maximization condition.