Bode integrals and laws of variety in linear control systems

Zhang, Hui; Sun, Youxian

doi:10.1109/acc.2003.1238915

Cited by 8 publications

(6 citation statements)

References 14 publications

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“…The second term in the right hand of Eqn (8) reflects the variation of time average information of the signal after it transmitted through the system F (z ), and was defined as the variety of system F (z ). [11] Denote it as…”

Section: Remarkmentioning

confidence: 99%

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On information transmission in linear feedback tracking systems

Zhang¹,

Sun²

2008

Asia-Pacific J Chem Eng

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Information transmission in discrete time linear time-invariant (LTI) feedback tracking systems was investigated by using measures of directed information and mutual information. It was proved that, for a pair of extraneous input and internal variable, directed information (rate) is always equal to mutual information (rate); for a pair of internal variables, the former is smaller than the latter. Furthermore, the feedback changes the information transmission between internal variables, while it has no influence on information transmission from extraneous variable to internal variable. Consideration on system design was discussed. 

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Section: Remarkmentioning

confidence: 99%

“…information transmission, entropy rate and mutual information rate play important roles in stochastic control and estimation problems. [6,8,11,12] However, the function of directed information (rate), which measures the real information transmission in causal systems, has not been discussed for control.…”

Section: Introductionmentioning

confidence: 99%

On information transmission in linear feedback tracking systems

Zhang¹,

Sun²

2008

Asia-Pacific J Chem Eng

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“…Specifically, the work in [5] dealt with the tracking issues without a channel in the feedback link, while [1] dealt with disturbance rejection. A result in [5] shows that a necessary condition for efficient tracking is that the information flow from the reference signal to the output should be greater than the information flow between the disturbance and the output. We know that in the absence of noise and without a communication channel in the feedback loop, the mutual information rate (or information rate) between reference signal and the output is infinite.…”

Section: Introductionmentioning

confidence: 99%

Limitations in tracking systems

Hurtado

Abdallah²,

Jayaweera³

2010

J. Control Theory Appl.

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In this paper, we obtain information theoretical conditions for tracking in linear time-invariant control systems. We consider the particular case where the closed loop contains a channel in the feedback loop. The mutual information rate between the feedback signal and the reference input signal is used to quantify information about the reference signal that is available for feedback. This mutual information rate must be maximized in order to improve the tracking performance. The mutual information is shown to be upper bounded by a quantity that depends on the unstable eigenvalues of the plant and on the channel capacity. If the channel capacity reaches a lower limit, the feedback signal becomes completely uncorrelated with the reference signal, rendering feedback useless. We also find a lower bound on the expected squared tracking error in terms of the entropy of a random reference signal. We show a misleading case where the mutual information rate does not predict the expected effect of nonminimum phase zeros. However, mutual information rate helps generalize the concept that there is a tradeoff when tracking and disturbance rejection are simultaneous goals, and a constraint communication channel is present in the feedback loop. Examples and simulations are provided to demonstrate some of the results.

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“…Previous related work in [3], [5], [6], [13], [14], [15] and [16] detailed some aspects of performance and limitations of control systems in terms of information theoretic quantities. Specifically, the work in [14] dealt with the tracking issues without a channel in the feedback link, while [3] dealt with disturbance rejection.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, the work in [14] dealt with the tracking issues without a channel in the feedback link, while [3] dealt with disturbance rejection. A result in [14], shows that a necessary condition for efficient tracking is that the information flow from the reference signal to the output should be greater than the information flow between the disturbance and the output. We know that in the absence of noise, and without a communication channel in the feedback loop, the mutual information rate (or information rate) between reference signal and the output is infinite.…”

Section: Introductionmentioning

confidence: 99%

Conditions for tracking in networked control systems

López

Abdallah

Jayaweera

et al. 2008

2008 47th IEEE Conference on Decision and Control

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Abstract-In this paper we obtain information theoretical conditions for tracking in linear time-invariant control systems. We consider the particular case where the closed loop contains a channel in the feedback loop. The mutual information rate between the feedback signal and the reference input signal is used to quantify information about the reference signal that is available for feedback. This mutual information rate must be maximized in order to improve the tracking performance. The mutual information is shown to be upper bounded by a quantity that depends on the unstable eigenvalues of the plant and on the channel capacity. If the channel capacity reaches a lower limit, the feedback signal becomes completely uncorrelated with the reference signal, rendering feedback useless. We also find a lower bound on the expected squared tracking error in terms of the entropy of a random reference signal. Examples and simulations are provided to demonstrate the results.

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Bode integrals and laws of variety in linear control systems

Cited by 8 publications

References 14 publications

On information transmission in linear feedback tracking systems

On information transmission in linear feedback tracking systems

Limitations in tracking systems

Conditions for tracking in networked control systems

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