Observer-based event-triggered boundary control of a linear 2 × 2 hyperbolic systems

Espitia, Nicolás

doi:10.1016/j.sysconle.2020.104668

Cited by 47 publications

(27 citation statements)

References 32 publications

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“…Proof Motivated by References 1,19, define

h (t) = \frac{ε ρ (U (t) - U_{c} (t))^{2} + (1 - α) η (t)}{- α η (t)} .

Moreover, integrating both sides of (16) from 0 to t , it gives

η (t) = {true\int}_{0}^{t} (ρ \overset{true‾}{λ} (U (s) - U_{c} (s))^{2} - θ (‖ X (s) ‖^{2} + ‖ w (\cdot, s) ‖_{L^{2}}^{2} + w^{2} (0, s))) d s + η_{0},

which means that

η (t)

is continuous for any

t \geq 0

. By the strict negativity and continuity of

η (t)

, it follows that

h (t)

is continuous on

[t_{k}, t_{k + 1})

.…”

Section: Stability Analysismentioning

confidence: 99%

“…Despite many results on the event‐triggered control problems of uncertain ODE systems (see, e.g., References 6–8 and references therein), the associated control design and performance analysis therein are essentially different from those for PDE‐ODE cascade systems. Moreover, although some results on the event‐triggered control problems of pure hyperbolic PDE systems and sandwiched hyperbolic PDE systems have been, respectively, obtained in works 1,2,19 and work, 22 the coexistence of the ODE and PDE subsystems and the presence of nonlocal term make the key techniques in this article, including the infinite‐dimensional backstepping transformations and the construction of Lyapunov function for stability analysis, extremely different from those in References 1,2,19,22. (iii) A novel event‐triggered control scheme is proposed for uncertain hyperbolic PDE‐ODE cascade systems .…”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

“…Recently, the event‐triggered control of PDE systems has received increasing attentions 1–3,12–22 . Particularly, the event‐triggered stabilization of hyperbolic and parabolic PDE systems is investigated in works 1,2,18–22 and works, 3,13–17 respectively. However, the systems therein all require the parameters to be exactly known, which greatly limits the application scope of the existing results.…”

Section: Introductionmentioning

confidence: 99%

“…We would like to highlight the contributions of this article in the following threefold: (i) The presence of unknown parameters makes the system under investigation essentially different from those in the related literature . In the existing works, 1–3,13–22 all the systems therein do not allow unknown system parameters, which makes the traditional control approaches cannot achieve the event‐triggered stabilization of system (1). In fact, to the authors' knowledge, the present article is the first attempt to consider the adaptive event‐triggered stabilization of distributed parameter systems with unknown parameters.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive event‐triggered control for a class of uncertain hyperbolic PDE‐ODE cascade systems

Liu

et al. 2021

Intl J Robust & Nonlinear

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This article investigates the event‐triggered stabilization for a class of hyperbolic PDE‐ODE cascade systems with nonlocal term. The presence of unknown parameters in the system brings technical challenges from design to analysis. This compels us to integrate certain powerful dynamic compensation into event‐triggering control mechanism. To solve the problem, by adaptive technique, a compensation strategy is developed to counteract the parametric uncertainties. Then, a desired event‐triggered controller is delicately designed to guarantee that all the signals in the closed‐loop system are bounded and the original system states converge to zero in the L2 norm. Particularly, the event‐triggering mechanism with an additional dynamic signal in the threshold is devised to overcome the negative influence of execution error, while ensuring a positive lower bound for the interexecution intervals. Finally, a simulation example is given to illustrate the effectiveness of the proposed control strategy.

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“…Proof Motivated by References 1,19, define

h (t) = \frac{ε ρ (U (t) - U_{c} (t))^{2} + (1 - α) η (t)}{- α η (t)} .

Moreover, integrating both sides of (16) from 0 to t , it gives

η (t) = {true\int}_{0}^{t} (ρ \overset{true‾}{λ} (U (s) - U_{c} (s))^{2} - θ (‖ X (s) ‖^{2} + ‖ w (\cdot, s) ‖_{L^{2}}^{2} + w^{2} (0, s))) d s + η_{0},

which means that

η (t)

is continuous for any

t \geq 0

. By the strict negativity and continuity of

η (t)

, it follows that

h (t)

is continuous on

[t_{k}, t_{k + 1})

.…”

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Adaptive event‐triggered control for a class of uncertain hyperbolic PDE‐ODE cascade systems

Liu

et al. 2021

Intl J Robust & Nonlinear

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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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Event-Triggered Output Feedback Control of Traffic Flow on Cascaded Roads

Espitia

Auriol²,

Yu³

et al. 2022

Advances in Distributed Parameter Systems

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Observer-based event-triggered boundary control of a linear 2 × 2 hyperbolic systems

Cited by 47 publications

References 32 publications

Adaptive event‐triggered control for a class of uncertain hyperbolic PDE‐ODE cascade systems

Adaptive event‐triggered control for a class of uncertain hyperbolic PDE‐ODE cascade systems

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

Event-Triggered Output Feedback Control of Traffic Flow on Cascaded Roads

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