Event triggered control of two time scale system

doi:10.1109/INDIANCC.2017.7846493

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Event triggered control of two time scale system

Proceedings Article•DOI•

Event triggered control of two time scale system

Manisha Bhandari¹, Deepak Fulwani², Rajeev Gupta¹•Institutions (2)

Rajasthan Technical University¹, Indian Institute of Technology, Jodhpur²

01 Jan 2017-Vol. 2017, pp 309-314

TL;DR: It is proved that the closed loop system asymptotically converges to an adjustable region around the equilibrium point and a minimum bound on inter-execution time is also guaranteed.

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Abstract: This paper describes the framework for event triggered control of a plant possessing two time scales. The periodic sampling requirement is relaxed and states are sampled based on a triggering rule. The dynamic trigger function where event triggering threshold varies with time has been used. Triggering function parameters are different for slow and fast states and events are detected independently in the two subsystems. This also allows the sensors for slow and fast states to be geographically distributed in the network. Further singular perturbation technique is used to decouple the system into fast and slow subsystems and stability of the overall system is investigated. It is proved that the closed loop system asymptotically converges to an adjustable region around the equilibrium point and a minimum bound on inter-execution time is also guaranteed. Asymptotic stability may also be obtained if the parameters of trigger function are adequately selected. Simulation results manifest the efficacy of the proposed approach and verify the theoretical analysis.

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Citations

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Comparison of Riemann and Lebesque sampling for first order stochastic systems

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Karl Johan Åström, Bo Bernhardsson

01 Jan 2002

TL;DR: In this article, it is shown that Lebesgue sampling gives better performance for some simple systems than traditional Riemann sampling, which is an analog of integration theory and is called event-based sampling.

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Abstract: The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

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77 citations

Journal Article•DOI•

Event-Triggered Composite Control of a Two Time Scale System

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Manisha Bhandari¹, Deepak Fulwani², Rajeev Gupta¹•Institutions (2)

Rajasthan Technical University¹, Indian Institute of Technology, Jodhpur²

01 Apr 2018-IEEE Transactions on Circuits and Systems Ii-express Briefs

TL;DR: The theory of singular perturbation is used to decouple the system into slow and fast subsystems, and stability of the system is established and the proposed control strategy guarantees convergence of system states to an adjustable region around origin excluding the Zeno behavior.

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Abstract: This brief proposes an event-triggered composite control of a two time scale system. A periodic sampling requirement is relaxed and both slow and fast states of the system decide independently when transmitting their current measurements based on a time-dependent triggering rule. The distinct feature of this scheme is that it does not require synchronized measurement updates of its slow and fast dynamics. Further, the theory of singular perturbation is used to decouple the system into slow and fast subsystems, and stability of the system is established. The proposed control strategy guarantees convergence of system states to an adjustable region around origin excluding the Zeno behavior. Simulation results manifest the effectiveness of the proposed approach.

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38 citations

Cites background from "Event triggered control of two time..."

...In [12] ETC of a linear TTSS is studied....
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...In place of using full state information to determine the triggering instances (such as in [3]–[5] and [12] etc....
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Journal Article•DOI•

Model-based dual-stage event-triggered control of linear system with two time scales

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Xiang Ren¹, Fei Hao¹•Institutions (1)

Beihang University¹

11 Feb 2020-International Journal of Systems Science

TL;DR: The singular perturbation technique is used to analyse the stability of the event-triggered control closed-loop system with a dual-stage event-triggering condition and the relations between the parameters in the events can be selected in a range independent of the matrices in the model.

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Abstract: In this paper, the model-based event-triggered control is addressed for a class of linear systems with two time scales. The singular perturbation technique is used to analyse the stability of the e...

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2 citations

Cites background from "Event triggered control of two time..."

...where the matrix A22 is supposed to be invertible and the same assumption was used in Bhandari et al. (2018). Based on the expressions ofH andL in (8), the dynamics of the states (ξT , ηT)T can be written as ( ξ̇...
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...In Bhandari, Fulwani, and Gupta (2017) and Bhandari, Fulwani, and Gupta (2018), the event-triggered control of both the slow and fast dynamics was implemented for linear systems, where the event-triggering condition utilised a time-varying threshold....
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Proceedings Article•DOI•

Event-trigger Control of Discrete Two-time Scale System by Leveraging its Intrinsic Properties

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poonam sahu¹, Manisha Bhandari², Deepak Fulwani¹•Institutions (2)

Indian Institute of Technology, Jodhpur¹, Rajasthan Technical University²

01 Jun 2019

TL;DR: This work proposes an event-trigger theory which leverages the physical property of discrete two-time scale system to reduce the requirement of network bandwidth.

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Abstract: There are several physical systems which exhibit two-time scale property. When these systems are controlled through networks, uniform sampling causes an extra burden on the network bandwidth. Furthermore, uniform sampling of slow and fast variables leads to over-sampling of slow variables. This work proposes an event-trigger theory which leverages the physical property of discrete two-time scale system to reduce the requirement of network bandwidth. Events in slow and fast variables occur as per their respective dynamics and based on the occurrence of a respective event, only slow or fast variables are communicated through a network. Thus the communication of the state is carried out based on an event of the respective set of variables. Simulation studies are presented to validate the theoretical developments.

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1 citations

Cites background from "Event triggered control of two time..."

...Asynchronous sampling provides key points of interest over time-triggered sampling in terms of network utilization and communication load [14]....
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Proceedings Article•DOI•

Event triggered control of singularly perturbec linear system based on its slow and fast model

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Manisha Bhandari¹, Deepak Fulwani², Rajeev Gupta¹•Institutions (2)

Rajasthan Technical University¹, Indian Institute of Technology, Jodhpur²

22 Mar 2017

TL;DR: The stability properties of overall closed loop system is studied and it is found that for sufficiently small value of singular perturbation parameter, system attains practical stability and by adequately selecting trigger function parameters, asymptotic stability is also achieved.

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Abstract: In this paper, we consider the event triggered control of the singularly perturbed linear system, where the communication between sensor and the controller/actuator is through a digital communication network and the transmission is based on some state dependent criterion. The models of slow and fast subsystems of the plant are added at the controller and are used for the estimation of states between the transmission times. Whenever the difference between estimated and actual states exceeds a certain threshold, controller is updated with the actual states of the plant provided by the sensor. This effectively reduces the communication frequency. The stability properties of overall closed loop system is studied and it is found that for sufficiently small value of singular perturbation parameter, system attains practical stability and by adequately selecting trigger function parameters, asymptotic stability is also achieved. A numerical example is shown to illustrate the results of the paper.

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Cites background or result from "Event triggered control of two time..."

...Model-Based Event Triggered Control In the majority of event-triggered control systems in the literature, the controller is a typical sampled data controller which generates a piece-wise constant input by keeping the received measurements constant till the arrival of new measurements at the next sampling instant [3], [16]....
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...Proof: This proof is in line with [16]....
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...In a recent work [16] ETC of linear SPS is discussed....
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References

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Proceedings Article•DOI•

On model-based networked control of singularly perturbed systems

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Wang Gexia¹, Wang Zhiming¹, D.S. Naidu²•Institutions (2)

East China Normal University¹, Idaho State University²

16 Jul 2008

TL;DR: In this article, the state feedback control of the linear singularly perturbed plant is studied, where the sensor and the controller/actuator are connected via a network and the transmission frequency is constant.

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Abstract: In this paper, the state feedback control of the linear singularly perturbed plant is studied, where the sensor and the controller/actuator are connected via a network and the transmission frequency is constant. In terms of the model-based control, the model plant in the singularly perturbed system is added at the controller/actuator to stabilize the original singularly perturbed system with periodically updating its state by the actual state of the plant provided by the sensor. Moreover, under some certain conditions, independent of the small parameter, the existence of the bound of the small parameter is shown to guarantee the globally exponential stability of the whole closed-loop singularly perturbed system. In addition, a numerical simulation is shown to illustrate the results of the paper.

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16 citations

"Event triggered control of two time..." refers background or methods in this paper

...0 0 0 1 u (29) Here n = 2 and m = 2 and control is designed using composite control technique defined in [6] as u = ( −1 −0.86 ) x1 + ( −0.18 −0.05 ) x2 (30) So that both Λ0 and Λ22 are Hurwitz....
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...As Λ22 is Hurwitz, hence it is non singular, and (9) is in standard singularly perturbed form....
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...The following controller is designed u(t) = K1x1(t)+K2x2(t) (5) so as to ensure satisfactory closed loop response, where K = [K1,K2] is such that both slow manifold Λ0 =(A11+B1K1)− (A12 +B1K2)(A22 +B2K2) −1(A21 +B2K1) and fast manifold (A22 +B2K2) of closed loop system (4) are Hurwitz stable....
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...Slow subsystem is given as ẋs(t) = A0.xs(t), (2) where xs(0) = x 0 1 and A0 = A11 −A12A −1 22 A21, and the fast subsystem with τ = ( tε ) dx f (τ) dτ = A22x f (τ) (3) where x f (0) = x 0 2 +A −1 22 A21x 0 1 Lemma 1: If P is a Hurwitz matrix and P0 is a constant matrix then there exists a sufficiently small λ such that (P+λ P0) is also a Hurwitz matrix....
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...Lemma 1 is about a property of Hurwitz matrix which says that small bounded perturbation of Hurwitz matrix is also Hurwitz [9]....
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Journal Article•DOI•

Stabilisation of two-time scale systems with a finite feedback data rate [Brief Paper]

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Zhiming Wang¹, G. Wang², Wei Liu¹•Institutions (2)

East China Normal University¹, Shanghai University of Electric Power²

29 Nov 2010-Iet Control Theory and Applications

TL;DR: There exists a bound of the small parameter such that the original two-time scale systems are stabilised by a quantised state via a finite feedback data rate channel for a small parameter within the bound.

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Abstract: This study investigates a stabilisation problem of two-time scale systems with a finite feedback data rate. The uniform estimate of the state growth rate over each sampling interval is first provided, which is shown to be independent of the small parameter. Then, based on the given uniform estimate and the decoupled form of the two-time scale systems, the requirement, which is independent of the small parameter, on the necessary data rate for the channel is derived through the design of a quantiser. Based on this requirement, the authors obtain the detecting systems, which are two-time scale hybrid systems with impulsive. Then, under the assumption of strong controllability of the original two-time scale systems, it is shown that there exists a bound of the small parameter such that the original two-time scale systems are stabilised by a quantised state via a finite feedback data rate channel for a small parameter within the bound. Finally, a simulation example illustrates the result.

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8 citations

"Event triggered control of two time..." refers background in this paper

...Similarly [10] deals with two-timescale system (TTSS) and a derives a necessary data rate for feedback channel independent of the small parameter so that the plant is stable....
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