Bit Rate Conditions to Stabilize a Continuous-Time Scalar Linear System Based on Event Triggering

Ling, Qiang

doi:10.1109/tac.2016.2618000

Cited by 74 publications

(54 citation statements)

References 27 publications

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“…

{\overset{x}{true}}_{d} false(t false)

and u ( t ) are generated as

\frac{d}{d t} {\overset{x}{true}}_{d} false(t false) = λ_{0} {\overset{x}{true}}_{d} false(t false) + u false(t false), {\overset{x}{true}}_{d} false(0 false) = 0,

u false(t false) = - G {\overset{x}{true}}_{d} false(t false),

where

{\overset{x}{true}}_{d} false(t false)

is reset with the received θ k at time

r_{k}^{'}

( r k in the global clock) and the control gain G is chosen to satisfy

λ_{0} + {normalΔ}_{λ} - G < 0 .

Define

\overset{λ}{true} = λ - G

and

{\overset{λ}{true}}_{0} = λ_{0} - G

. Then,

{\overset{λ}{true}}_{0} - {normalΔ}_{λ} \leq \overset{λ}{true} \leq {\overset{λ}{true}}_{0} + {normalΔ}_{λ} < 0 .

Compared with the constraint of − λ < λ − G <0 in our previous work, more freedom is given to the design of G in , which may lower the required stabilizing bit rate as shown later.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…Similarly,

{\overset{x}{true}}_{e} false(t false)

is reset with the obtained θ k at time t k . The estimation error of

{\overset{x}{true}}_{e} false(t false)

is denoted as

{\overset{x}{true}}_{e} false(t false) = x false(t false) - {\overset{x}{true}}_{e} false(t false) .

According to and , we know that

{\overset{x}{true}}_{e} false(t false)

is governed by

\frac{d}{d t} {\overset{x}{true}}_{e} false(t false) = λ {\overset{x}{true}}_{e} false(t false) + normalΔ λ \times {\overset{x}{true}}_{e} false(t false) + G ((), {\overset{x}{true}}_{e} false(t false) - {\overset{x}{true}}_{d} false(t false)) + w false(t false) .

Compared with our previous work, the state estimation error dynamics in includes one extra term,

normalΔ λ \times {\overset{x}{true}}_{e} false(t false)

, which results from the system matrix uncertainty and increases the stabilizing bit rate.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…Compared with two exceptions in the aforementioned works, our stabilizing bit rate is finite and may be lower than the one in the work of Montestrue and Antsaklis and R 0 in by extracting state information not only from the bits inside feedback packets but also from the receive time instants of feedback packets. Compared with the concerned system in our previous work, our system suffers from system matrix uncertainty that behaves quite different from the quantization error and the process noise and cannot be simply handled by the methods in our previous work . To resolve this system matrix uncertainty issue, this paper develops new methods, which are more efficient and more complicated than the ones in our previous work .…”

Section: Introductionmentioning

confidence: 97%

“…Compared with the concerned system in our previous work, our system suffers from system matrix uncertainty that behaves quite different from the quantization error and the process noise and cannot be simply handled by the methods in our previous work . To resolve this system matrix uncertainty issue, this paper develops new methods, which are more efficient and more complicated than the ones in our previous work . The performance advantages of this paper will be demonstrated through some examples in the simulation section. Clock offset: Besides the processing and network delays, the clock offset between the sensor and the controller further perturbs the difference between the sampling time instants and the receive time instants of feedback signals.…”

Section: Introductionmentioning

confidence: 98%

“…When the sampling time instants of feedback signals can be perfectly known by the controller, ie, there is neither processing nor network delays, the asymptotic stability can be achieved by transmitting a finite number of bits, which means the stabilizing bit rate is actually 0. In our previous works, we quantitatively investigated the effects of bounded processing delay and bounded network delay on stabilizing bit rates. These event‐triggered stabilizing bit rate conditions are extended by this paper in the following two aspects.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bit rate conditions to stabilize an uncertain scalar continuous‐time linear system with clock offset

Ling

Chen

Dou

2019

Intl J Robust & Nonlinear

Self Cite

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Summary This paper aims to stabilize a scalar continuous‐time linear system that transmits its feedback information through a digital communication network. The finite bit rate of the feedback network plays a critical role in the input‐to‐state stability of that system. Stabilizing bit rate conditions depend on not only the system matrix but also the uncertainty of the system matrix and the unknown clock offset between the transmitter (sensor) and the receiver (controller). Compared with the current literature, this paper can handle the system matrix uncertainty and clock offset through implementing an event‐triggered sampling strategy and derive stabilizing conditions that require lower bit rates than those of periodic sampling strategies. Such bit rate saving mainly comes from the fact that our event‐triggered strategy can extract state information from the receive time instants of feedback packets without any extra communication cost. Simulations are done to confirm the effectiveness of the obtained stabilizing bit rate conditions.

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“…

{\overset{x}{true}}_{d} false(t false)

and u ( t ) are generated as

\frac{d}{d t} {\overset{x}{true}}_{d} false(t false) = λ_{0} {\overset{x}{true}}_{d} false(t false) + u false(t false), {\overset{x}{true}}_{d} false(0 false) = 0,

u false(t false) = - G {\overset{x}{true}}_{d} false(t false),

where

{\overset{x}{true}}_{d} false(t false)

is reset with the received θ k at time

r_{k}^{'}

( r k in the global clock) and the control gain G is chosen to satisfy

λ_{0} + {normalΔ}_{λ} - G < 0 .

Define

\overset{λ}{true} = λ - G

and

{\overset{λ}{true}}_{0} = λ_{0} - G

. Then,

{\overset{λ}{true}}_{0} - {normalΔ}_{λ} \leq \overset{λ}{true} \leq {\overset{λ}{true}}_{0} + {normalΔ}_{λ} < 0 .

Compared with the constraint of − λ < λ − G <0 in our previous work, more freedom is given to the design of G in , which may lower the required stabilizing bit rate as shown later.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…Similarly,

{\overset{x}{true}}_{e} false(t false)

is reset with the obtained θ k at time t k . The estimation error of

{\overset{x}{true}}_{e} false(t false)

is denoted as

{\overset{x}{true}}_{e} false(t false) = x false(t false) - {\overset{x}{true}}_{e} false(t false) .

According to and , we know that

{\overset{x}{true}}_{e} false(t false)

is governed by

\frac{d}{d t} {\overset{x}{true}}_{e} false(t false) = λ {\overset{x}{true}}_{e} false(t false) + normalΔ λ \times {\overset{x}{true}}_{e} false(t false) + G ((), {\overset{x}{true}}_{e} false(t false) - {\overset{x}{true}}_{d} false(t false)) + w false(t false) .

Compared with our previous work, the state estimation error dynamics in includes one extra term,

normalΔ λ \times {\overset{x}{true}}_{e} false(t false)

, which results from the system matrix uncertainty and increases the stabilizing bit rate.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bit rate conditions to stabilize an uncertain scalar continuous‐time linear system with clock offset

Ling

Chen

Dou

2019

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

A control scheme for interval type‐2 T‐S fuzzy systems at constrained bit rates: A coding and decoding scheme

Yan,

Zhang,

2024

Asian Journal of Control

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SummaryThis study focuses on a class of interval type‐2 T‐S fuzzy systems under bit rate constraint(BRC), which can adapt to complex systems more flexibly than the traditional interval type‐1 T‐S fuzzy model. In order to guarantee the security of data transmission, and considering that the channel is affected by the bit rate during transmission, this study introduces a codec scheme in the interval type‐2 T‐S fuzzy system and applies it to the channel from the sensor to the controller. With the support of the codec scheme, this study explores the sufficient conditions to satisfy the data recoverability, and based on the satisfaction of these conditions, the system is proposed to satisfy the sufficient conditions for input‐to‐state stability (ISS) and the controller gain. Through the in‐depth analysis in this paper, this study proposes a control scheme that can fit complex systems more accurately and also confirms the importance of considering bit rate constraints in communication systems. Finally, the paper is validated by simulation with two specific examples, which fully demonstrate the superiority and effectiveness of the proposed control scheme.

show abstract

Stabilization of switched nonlinear systems with dynamic output quantization and disturbances

Lian

2020

Intl J Robust & Nonlinear

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Summary This paper studies the problem of quantized output feedback stabilization for a disturbed discrete‐time switched system. With the quantized output measurement, an extended state current estimator is constructed to estimate the state and disturbance. In the presence of switches and disturbances, the design of quantization scheme becomes a big challenge to avoid the quantizer saturation and guarantee the control precision. In this setup, the well‐applied time‐triggered method to design the update policy of dynamic quantization parameter is hard to implement. We solve the above problem by proposing a novel event‐triggered update policy of quantization parameter, by which the quantizer update is adaptive to the switching signal and the bound of disturbance difference. Consequently, the quantizer saturation is avoided and, combined with the designed dwell‐time switching law, the system state can converge to the origin. The proposed method is illustrated by a numerical example.

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Bit Rate Conditions to Stabilize a Continuous-Time Scalar Linear System Based on Event Triggering

Cited by 74 publications

References 27 publications

Bit rate conditions to stabilize an uncertain scalar continuous‐time linear system with clock offset

Bit rate conditions to stabilize an uncertain scalar continuous‐time linear system with clock offset

A control scheme for interval type‐2 T‐S fuzzy systems at constrained bit rates: A coding and decoding scheme

Stabilization of switched nonlinear systems with dynamic output quantization and disturbances

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