Abstract

A new double closed-loop control system with mean-square exponential stability is firstly proposed to optimize the detection accuracy and dynamic response characteristic of the integrated optical resonance gyroscope (IORG). The influence mechanism of optical nonlinear effects on system detection sensitivity is investigated to optimize the demodulation gain, the maximum sensitivity and the linear work region of a gyro system. Especially, we analyze the effect of optical parameter fluctuation on the parameter uncertainty of system, and investigate the influence principle of laser locking-frequency noise on the closed-loop detection accuracy of angular velocity. The stochastic disturbance model of double closed-loop IORG is established that takes the unfavorable factors such as optical effect nonlinearity, disturbed disturbance, optical parameter fluctuation and unavoidable system noise into consideration. A robust control algorithm is also designed to guarantee the mean-square exponential stability of system with a prescribed H performance in order to improve the detection accuracy and dynamic performance of IORG. The conducted experiment results demonstrate that the IORG has a dynamic response time less than 76us, a long-term bias stability 7.04°/h with an integration time of 10s over one-hour test, and the corresponding bias stability 1.841°/h based on Allan deviation, which validate the effectiveness and usefulness of the proposed detection scheme.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  14. Y. Zhi, L. Feng, M. Lei, and K. Wang, “Low-delay, high-bandwidth frequency-locking loop of resonator integrated optic gyro with triangular phase modulation,” Appl. Opt. 52(33), 8024–8031 (2013).
    [Crossref] [PubMed]
  15. J. Wang, L. Feng, Y. Zhi, H. Liu, W. Wang, and M. Lei, “Reduction of backreflection noise in resonator micro-optic gyro by integer period sampling,” Appl. Opt. 52(32), 7712–7717 (2013).
    [Crossref] [PubMed]
  16. J. Wu, M. Smiciklas, L K. Strandjord, T. Qiu, W. Ho and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers”, International Society for Optics and Photonics 2015: 96341O–96341O–4.
  17. H. Ma, J. Zhang, L. Wang, and Z. Jin, “Double closed-loop resonant micro optic gyro using hybrid digital phase modulation,” Opt. Express 23(12), 15088–15097 (2015).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  20. D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
    [Crossref]
  21. T. Liu, J. Zhao, and J. H. David, “Exponential synchronization of complex delayed dynamical networks with switching topology,” IEEE Trans. Circuits Syst. I, Reg. Papers 57(11), 2967–2980 (2010).
  22. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishinan, “Linear Matrix Inequalities in Systems and Control Theory,” Philadelphia, PA, USA: SIAM, (1994).
  23. B. Shen, Z. Wang, and H. Shu, “Distributed H1-consensus Filtering in Sensor Networks with Multiple Missing Measurements: The Finite-horizon Case,” Automatica 64(46), 1682–1688 (2010).
    [Crossref]
  24. W. Deng, H. Li, C. Zhang, and P. Wang, “Optimization of Detection Accuracy of Closed-Loop Optical Voltage Sensors Based on Pockels Effect,” Sensors (Basel) 17(8), 1723 (2017).
    [Crossref] [PubMed]
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2017 (2)

W. Liang, V. S. Ilchenko, A. A. Savchenkov, E. Dale, D. Eliyahu, A. B. Matsko, and L. Maleki, “Resonant micro photonic gyroscope,” Optica 4(1), 114–117 (2017).
[Crossref]

W. Deng, H. Li, C. Zhang, and P. Wang, “Optimization of Detection Accuracy of Closed-Loop Optical Voltage Sensors Based on Pockels Effect,” Sensors (Basel) 17(8), 1723 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (2)

2014 (1)

2013 (3)

2012 (2)

D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
[Crossref]

M. Á. Guillén-Torres, E. Cretu, N. A. F. Jaeger, and L. Chrostowski, “Ring resonator optical gyroscopes-Parameter optimization and robustness analysis,” J. Lightwave Technol. 30(12), 1802–1817 (2012).
[Crossref]

2011 (1)

L. Hong, C. Zhang, L. Feng, M. Lei, and H. Yu, “Effect of phase modulation nonlinearity in resonator micro-optic gyro,” Opt. Eng. 50(9), 094404 (2011).
[Crossref]

2010 (4)

T. Liu, J. Zhao, and J. H. David, “Exponential synchronization of complex delayed dynamical networks with switching topology,” IEEE Trans. Circuits Syst. I, Reg. Papers 57(11), 2967–2980 (2010).

B. Shen, Z. Wang, and H. Shu, “Distributed H1-consensus Filtering in Sensor Networks with Multiple Missing Measurements: The Finite-horizon Case,” Automatica 64(46), 1682–1688 (2010).
[Crossref]

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photonics 2(3), 370–404 (2010).
[Crossref]

X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90 ° polarization-axis rotated splices,” Opt. Express 18(2), 1677–1683 (2010).
[Crossref] [PubMed]

2008 (1)

2001 (1)

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors 1(4), 332–339 (2001).
[Crossref]

1997 (1)

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15(3), 466–473 (1997).
[Crossref]

1980 (1)

Armenise, M. N.

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photonics 2(3), 370–404 (2010).
[Crossref]

Barbour, N.

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors 1(4), 332–339 (2001).
[Crossref]

Campanella, C. E.

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photonics 2(3), 370–404 (2010).
[Crossref]

Chrostowski, L.

Ciminelli, C.

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photonics 2(3), 370–404 (2010).
[Crossref]

Cretu, E.

Dale, E.

David, J. H.

T. Liu, J. Zhao, and J. H. David, “Exponential synchronization of complex delayed dynamical networks with switching topology,” IEEE Trans. Circuits Syst. I, Reg. Papers 57(11), 2967–2980 (2010).

Dell’Olio, F.

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photonics 2(3), 370–404 (2010).
[Crossref]

Deng, W.

W. Deng, H. Li, C. Zhang, and P. Wang, “Optimization of Detection Accuracy of Closed-Loop Optical Voltage Sensors Based on Pockels Effect,” Sensors (Basel) 17(8), 1723 (2017).
[Crossref] [PubMed]

Eliyahu, D.

Feng, L.

Guillén-Torres, M. Á.

Haavisto, J.

Harumoto, M.

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15(3), 466–473 (1997).
[Crossref]

He, Z.

Hong, L.

L. Hong, C. Zhang, L. Feng, M. Lei, and H. Yu, “Effect of phase modulation nonlinearity in resonator micro-optic gyro,” Opt. Eng. 50(9), 094404 (2011).
[Crossref]

Hotate, K.

Ilchenko, V. S.

Jaeger, N. A. F.

Jiao, H.

Jin, Z.

Lei, M.

Li, H.

W. Deng, H. Li, C. Zhang, and P. Wang, “Optimization of Detection Accuracy of Closed-Loop Optical Voltage Sensors Based on Pockels Effect,” Sensors (Basel) 17(8), 1723 (2017).
[Crossref] [PubMed]

L. Feng, J. Wang, Y. Zhi, Y. Tang, Q. Wang, H. Li, and W. Wang, “Transmissive resonator optic gyro based on silica waveguide ring resonator,” Opt. Express 22(22), 27565–27575 (2014).
[Crossref] [PubMed]

Liang, W.

Liu, H.

Liu, T.

T. Liu, J. Zhao, and J. H. David, “Exponential synchronization of complex delayed dynamical networks with switching topology,” IEEE Trans. Circuits Syst. I, Reg. Papers 57(11), 2967–2980 (2010).

Livas, J.

Ma, H.

Maleki, L.

Matsko, A. B.

Numata, K.

Ong, C. J.

D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
[Crossref]

Pajer, G. A.

Savchenkov, A. A.

Schmidt, G.

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors 1(4), 332–339 (2001).
[Crossref]

Shen, B.

B. Shen, Z. Wang, and H. Shu, “Distributed H1-consensus Filtering in Sensor Networks with Multiple Missing Measurements: The Finite-horizon Case,” Automatica 64(46), 1682–1688 (2010).
[Crossref]

Shu, H.

B. Shen, Z. Wang, and H. Shu, “Distributed H1-consensus Filtering in Sensor Networks with Multiple Missing Measurements: The Finite-horizon Case,” Automatica 64(46), 1682–1688 (2010).
[Crossref]

Tang, Y.

Thorpe, J. I.

Wang, J.

Wang, K.

Wang, L.

Wang, P.

W. Deng, H. Li, C. Zhang, and P. Wang, “Optimization of Detection Accuracy of Closed-Loop Optical Voltage Sensors Based on Pockels Effect,” Sensors (Basel) 17(8), 1723 (2017).
[Crossref] [PubMed]

Wang, Q.

Wang, Q. G.

D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
[Crossref]

Wang, W.

Wang, X.

Wang, Z.

B. Shen, Z. Wang, and H. Shu, “Distributed H1-consensus Filtering in Sensor Networks with Multiple Missing Measurements: The Finite-horizon Case,” Automatica 64(46), 1682–1688 (2010).
[Crossref]

Wu, Z. G.

D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
[Crossref]

Yu, H.

L. Hong, C. Zhang, L. Feng, M. Lei, and H. Yu, “Effect of phase modulation nonlinearity in resonator micro-optic gyro,” Opt. Eng. 50(9), 094404 (2011).
[Crossref]

Yu, L.

D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
[Crossref]

Zhang, C.

W. Deng, H. Li, C. Zhang, and P. Wang, “Optimization of Detection Accuracy of Closed-Loop Optical Voltage Sensors Based on Pockels Effect,” Sensors (Basel) 17(8), 1723 (2017).
[Crossref] [PubMed]

L. Hong, C. Zhang, L. Feng, M. Lei, and H. Yu, “Effect of phase modulation nonlinearity in resonator micro-optic gyro,” Opt. Eng. 50(9), 094404 (2011).
[Crossref]

Zhang, D.

D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
[Crossref]

Zhang, J.

Zhao, J.

T. Liu, J. Zhao, and J. H. David, “Exponential synchronization of complex delayed dynamical networks with switching topology,” IEEE Trans. Circuits Syst. I, Reg. Papers 57(11), 2967–2980 (2010).

Zhi, Y.

Adv. Opt. Photonics (1)

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Photonic technologies for angular velocity sensing,” Adv. Opt. Photonics 2(3), 370–404 (2010).
[Crossref]

Appl. Opt. (3)

Automatica (1)

B. Shen, Z. Wang, and H. Shu, “Distributed H1-consensus Filtering in Sensor Networks with Multiple Missing Measurements: The Finite-horizon Case,” Automatica 64(46), 1682–1688 (2010).
[Crossref]

IEEE Sensors (1)

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors 1(4), 332–339 (2001).
[Crossref]

IEEE Trans. Circuits Syst. I, Reg. Papers (1)

T. Liu, J. Zhao, and J. H. David, “Exponential synchronization of complex delayed dynamical networks with switching topology,” IEEE Trans. Circuits Syst. I, Reg. Papers 57(11), 2967–2980 (2010).

J. Franklin Inst. (1)

D. Zhang, L. Yu, Q. G. Wang, C. J. Ong, and Z. G. Wu, “Exponential H∞ filtering for discrete-time singular switched system with time-varying delays,” J. Franklin Inst. 349(7), 2323 (2012).
[Crossref]

J. Lightwave Technol. (2)

Opt. Eng. (1)

L. Hong, C. Zhang, L. Feng, M. Lei, and H. Yu, “Effect of phase modulation nonlinearity in resonator micro-optic gyro,” Opt. Eng. 50(9), 094404 (2011).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Optica (1)

Sensors (Basel) (1)

W. Deng, H. Li, C. Zhang, and P. Wang, “Optimization of Detection Accuracy of Closed-Loop Optical Voltage Sensors Based on Pockels Effect,” Sensors (Basel) 17(8), 1723 (2017).
[Crossref] [PubMed]

Other (5)

S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishinan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia, PA, USA: SIAM, 1994.

J. Wu, M. Smiciklas, L K. Strandjord, T. Qiu, W. Ho and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers”, International Society for Optics and Photonics 2015: 96341O–96341O–4.

H. C. Lefevre, “The fiber-optic gyroscope,”. In French, Artech house, 1993, pp. 20–23.

S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishinan, “Linear Matrix Inequalities in Systems and Control Theory,” Philadelphia, PA, USA: SIAM, (1994).

N. Barbour, “Inertial Navigation Sensors [R],” Charles Stark Draper Lab Inc Cambridge ME, 2010.

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Figures (7)

Fig. 1
Fig. 1 The principle scheme of the double closed-loop IORG based on Sagnac effect. The triangular wave for phase modulation is applied on the upper arm and bottom arm of the IOPM. The feedback sawtooth wave is applied on the bottom arm of the IOPM. Meanwhile, the phase modulation triangular wave and digital feedback sawtooth wave are all differentially applied on the arms of the IOPM. The IOPM achieves the phase modulation and also enables the closed-loop control of AVTL.
Fig. 2
Fig. 2 The flow diagram of detected signals during the modulation and demodulation processes including (a) the interference intensity IT as a function of light frequency (b) the phase modulated carrier ϕ and equal frequency bias fbias; (c) the time-domain output Im of photoelectric detector after modulation; (d) the demodulated signal Id .
Fig. 3
Fig. 3 (a) the relationship between demodulation gain k1 and modulation frequency; (b)the demodulated signals Id shown as functions of frequency deviation for different modulation frequencies.
Fig. 4
Fig. 4 The block diagram of the double closed-loop detection scheme of IORG.
Fig. 5
Fig. 5 Implementation of the closed-loop IORG system. (a) The oscilloscope display of output signals under 300°/s rotational speed measurement. Curve A is the CW output which detected by PD2 and displayed on oscilloscope, Curve B is the CCW output which detected by PD1, and curve C is AVTL controller output; (b) the PD1 curve of LFLL; (c) the frequency locking noise of LFLL after the frequency of laser is locked to the center frequency of curve resonator (d) the step response of IORG system.
Fig. 6
Fig. 6 The results of measuring accuracy experiment of the IORG system. a) 1h test of bias stability; c) Allan variance of the 1h test data.
Fig. 7
Fig. 7 Results of scale factor experiment of the IORG system. a) the test of scale factor; b) The out curve and corresponding relative fitting error of the IORG system.

Tables (1)

Tables Icon

Table 1 The value of parameters of block diagram

Equations (28)

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Δ f Ω = D n e λ Ω
I T = I 0 ηβR 1+ q 2 2qcos2πfτ
I d ( f )= I 0 ηβR K qd 1+ q 2 2qcos2π( f+ f bias )τ I 0 ηβR K qd 1+ q 2 2qcos2π(f f bias )τ = 2msin2π f bias τ 1+ m 2 2 cos4π f bias τ+ m 2 2 cos4πfτ2mcos2πfτcos2π f bias τ I 0 ηβR K qd 1+ q 2 sin( 2πfτ )
I d ( f )=( k 1 +Δ k 1 )sin( 2πfτ )
f bias | k 1 f bias =0 = arccos 8 m 2 +1 1 2m 2πτ
I d 2 =( k 1 +Δ k 1 )sin( 2π( Δ f Ω +Δ f n )τ )
I d 2 =( k 1 +Δ k 1 )cos2πΔ f n τsin2πΔ f Ω τ+( k 1 +Δ k 1 )cos2πΔ f Ω τsin2πΔ f n τ
I d 2 ( Δf )=( k 2 +Δ k 2 )sin2πΔ f Ω τ+g( x 1 ( k ) ) v 2 ( k )
x 1 ( k+1 )= A 1 x 1 ( k )+ B 1 ( k 1 +Δ k 1 )sin( k f 1 K C 1 x 1 ( k ) )+ D 1 w 1 ( k )
x 2 ( k+1 )= A 2 x 2 ( k )+ B 2 ( k 2 +Δ k 2 )sin( k f 2 K C 2 x 2 ( k ) )+ B 2 g( x 1 ( k ) ) v 2 ( k )+ D 2 w 2 ( k )
x(k+1)=Ax(k)+ B ¯ f( k f 1 K C 1 x 1 (k), k f 2 K C 2 x 2 (k))+Ig( x 1 (k)) v 2 (k)+Dw(k)
( Φ+ ε 3 E T E ϕ 1 T P ϕ 2 T P 0 * P 0 PH * * P 0 * * * ε 3 I )<0
( Φ ˜ + ε 3 E T E ϕ ^ 1 T P ϕ ˜ 2 P 0 P 0 PH P 0 ε 3 I )<0
Φ ˜ =( αP+I ε 1 k f 1 2 H 1 K C 1 ε 2 k f 2 2 H 2 K C 2 0 ε 1 I 0 0 ε 2 I 0 γ 2 I ), ϕ ^ 1 =( A B D ), ϕ ˜ 2 =( σ G 0 H 1 0 0 ).
k 1 = 2 1+ N ad m I 0 ηRβ K Ga N dem ( 1+ q 2 ) V ref
f T ( K C i x i ( k ) )( f( K C i x i ( k ) ) K C i x i ( k ) )0, where i=1, 2.
E{ V( k+1 )αV( k ) }E{ x T ( k+1 )Px( k+1 )α x T ( k )Px( k ) ε 1 sin T ( K C 1 x 1 ( k ) )( sin( K C 1 x 1 ( k ) ) K C 1 x 1 ( k ) ) ε 2 sin T ( K C 2 x 2 ( k ) )( sin( K C 2 x 2 ( k ) ) K C 2 x 2 ( k ) ) }
E{ ( I ¯ g( x 1 ( k ) )v(k) ) T P( I ¯ g( x 1 ( k ) )v(k) ) }E{ x T ( k ) ( σ G 0 H 1 ) T P( σ G 0 H 1 )x( k ) }
E{ V( k+1 )αV( k ) }=E{ ς 1 T ( k ) ( ϕ ¯ 1 T P ϕ ¯ 1 ) ς 1 ( k )+ ς 1 T ( k )Φ ς 1 ( k ) + x T ( k ) ( σ G 0 H 1 ) T P( σ G 0 H 1 )x( k ) }
E{ V( k+1 )αV( k ) }E{ ς 1 T ( k )( ϕ ¯ 1 T P ϕ ¯ 1 + ϕ 2 T P ϕ 2 +Φ ) ς 1 ( k ) }
( Φ ϕ ¯ 1 T P ϕ 2 T P P ϕ ¯ 1 P 0 P ϕ 2 0 P )<0
( Φ ϕ ¯ 1 T P ϕ ¯ 2 T P P ϕ ¯ 1 P 0 P ϕ ¯ 2 0 P )=( Φ ϕ 1 T P ϕ 2 T P P ϕ 1 T P 0 P ϕ 2 0 P )+ M T F( k )N+ N T F T ( k )M<0
( Φ+ ε 3 E T E ϕ 1 T P ϕ 2 T P 0 * P 0 PH * * P 0 * * * ε 3 I )<0
E{ V( k+1 )αV( k )+Γ( k ) } E{ V( k+1 )αV( k )+Γ( k ) ε 1 f T ( K C 1 x 1 ( k ) )( sin( K C 1 x 1 ( k ) ) K C 1 x 1 ( k ) ) ε 2 f T ( K C 2 x 2 ( k ) )( sin( K C 2 x 2 ( k ) ) K C 2 x 2 ( k ) ) } =E{ ξ 2 T ( k )( ϕ ˜ 1 T P ϕ ˜ 1 ++ ϕ ˜ 2 T P ϕ ˜ 2 + Φ ˜ ) ξ 2 ( k ) }
ξ 2 (k)= ( x (k) T x (k1) T sin (Δφ(k)) T sin (Δφ(k1)) T w (k) T ) T
( Φ ˜ ϕ ˜ 1 T P ϕ ˜ 2 P P 0 P )<0
( Φ ˜ ϕ ^ 1 T P ϕ ˜ 2 P P 0 P )+ M 2 T F 2 ( k ) N 2 + N 2 T F 2 ( k ) M 2 ( Φ ˜ + ε 3 E T E ϕ ^ 1 T P ϕ ˜ 2 P 0 P 0 PH P 0 ε 3 I )<0
E{V(k+1)}<E{αV(k)Γ(k)}<E{ α k k 0 V( k 0 ) s= k 0 k α ks Γ(s) }

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