Delay robust state feedback stabilization of an underactuated network of two interconnected PDE systems

Auriol, Jean; Meglio, Florent Di; Bribiesca-Argomedo, Federico

doi:10.23919/acc.2019.8814858

Cited by 18 publications

(29 citation statements)

References 18 publications

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“…for any control law U (t) the closed-loop system (10)-(12) becomes unstable when there is an (arbitrarily small) delay δ > 0 in the loop. Adjusting the approach of [8] or [5], it can easily be shown, using the transport structure of the system, that the open loop system (5)- (8) in the absence of in-domain coupling terms has equivalent stability properties to those of the system defined on…”

Section: Problem Formulationmentioning

confidence: 99%

“…The design of the corresponding delay-robust control laws has been achieved using the backstepping approach to rewrite the considered systems as neutral systems with distributed delays [4,8] and adjusting the analysis methods developed for time delay systems [23,24]. Recently, this approach has been successfully used [5] to tackle the problem of delay robust state feedback stabilization of an underactuated network of two interconnected subsystems of two coupled PDEs. The proposed approach cannot be straightforwardly extended for a network composed of a higher number of subsystems due to the multiple interconnections.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed approach cannot be straightforwardly extended for a network composed of a higher number of subsystems due to the multiple interconnections. Moreover, the control law proposed in [5] requires the value of the state all over the spatial domain, which is unrealistic. To envision real applications, a state observer has to be designed.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we generalize the approach developed in [5] to an arbitrary number of interconnected subsystems of two linear coupled PDEs. Moreover, we provide a boundary observer that estimates the state in real time only using (collocated) boundary measurements.…”

Section: Introductionmentioning

confidence: 99%

“…To encompass the complex structure of the considered network, these backstepping transformations are not simple Volterra transformations. They have to act on all the states of the system (contrary to the case of two subsystems presented in [5]). In that sense, the idea behind such a transformation is similar to the one used in [16].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Output feedback stabilization of an underactuated cascade network of interconnected linear PDE systems using a backstepping approach

Auriol

2020

Automatica

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We detail in this article the development of a robust stabilizing output feedback control law for an underactuated cascade network of n systems of two heterodirectional linear first-order hyperbolic Partial Differential Equations interconnected through their boundaries. Only one of the subsystems is actuated. The proposed approach combines successive backstepping transformations that present a specific cascade structure. With these transformations it is possible to rewrite the original network system as a simple system for which all the in-domain coupling terms have been removed. One can then design a strictly proper stabilizing control law.The proposed control law is proved to be robust to small delays in the actuation. Finally, a boundary observer is designed, enabling stabilization by output feedback.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Output feedback stabilization of an underactuated cascade network of interconnected linear PDE systems using a backstepping approach

Auriol

2020

Automatica

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Traffic flow control on cascaded roads by event‐triggered output feedback

Espitia

Auriol

et al. 2022

Intl J Robust & Nonlinear

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In this article, we propose an event‐triggered output‐feedback controller that guarantees the simultaneous stabilization of traffic flow on two connected roads. The density and velocity traffic dynamics are described with the linearized Aw‐Rascle‐Zhang macroscopic traffic partial differential equation model, which results in a coupled hyperbolic system. The control objective is to simultaneously stabilize the upstream and downstream traffic to a given spatially uniform constant steady‐state that is in the congested regime. To suppress stop‐and‐go traffic oscillations on the cascaded roads, we consider a ramp metering strategy that regulates the traffic flow rate entering from the on‐ramp to the mainline freeway. The ramp metering is located at the outlet with only boundary measurements of flow rate and velocity. Under the event‐triggered scheme, the control signal is only updated when an event triggering condition is satisfied. Compared with the continuous input signal, the event‐triggered boundary output control presents a more realistic setting to implement by ramp metering on a digital platform. The event‐triggered control design relies on the emulation of the backstepping boundary output feedback and on a dynamic event‐triggered strategy to determine the time instants at which the control value must be updated. We prove that there is a uniform minimal dwell‐time (independent of initial conditions), thus avoiding the Zeno phenomenon. We guarantee the exponential convergence of the closed‐loop system under the proposed event‐triggered control. A numerical example illustrates the results.

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Simultaneous downstream and upstream output-feedback stabilization of cascaded freeway traffic

Auriol

Krstić

2022

Automatica

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Delay robust state feedback stabilization of an underactuated network of two interconnected PDE systems

Cited by 18 publications

References 18 publications

Output feedback stabilization of an underactuated cascade network of interconnected linear PDE systems using a backstepping approach

Output feedback stabilization of an underactuated cascade network of interconnected linear PDE systems using a backstepping approach

Traffic flow control on cascaded roads by event‐triggered output feedback

Simultaneous downstream and upstream output-feedback stabilization of cascaded freeway traffic

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