Output Tracking for One‐Dimensional Schrödinger Equation subject to Boundary Disturbance

Liu, Junjun; Wang, Jun‐Min; Guo, Yongfeng

doi:10.1002/asjc.1588

Cited by 11 publications

(15 citation statements)

References 28 publications

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“…This situation is different from the unstable case in [6], where there are at most finitely many unstable eigenvalues for the system to be controlled. The system (1.1) is different also from the one in [17], where the Schrödinger equation is essentially exponentially stable when the disturbance vanishes. Moreover…”

Section: Properties Of the System To Be Controlledmentioning

confidence: 99%

“…An interesting recent work is [16], where based on backstepping, the output tracking problem is considered for a general 2 × 2 system of first order linear hyperbolic PDEs, but no disturbances are taken into consideration. Adaptive control is used for output tracking for the Schrödinger equation in [17], where the system is exponentially stable and the disturbance acts at the boundary. For the optimal regularity, sharp uniform decay rates and observability of Schrödinger equations in several space dimensions, we refer to the work of Irena Lasiecka and collaborators [18,19,20,21].…”

Section: Introduction and Problem Formulationmentioning

confidence: 99%

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The regulation problem for the one-dimensional Schrödinger equation via the backstepping approach

Zhou

2016

2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE)

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We investigate the regulator problem (tracking and disturbance rejection) for a system (plant) described by a boundary controlled anti-stable linear one-dimensional Schrödinger equation, using the backstepping approach. The output to be controlled is not required to be measurable and its observation operator is assumed to be admissible for a certain operator semigroup that is related to the operator semigroup of the original plant. We consider both the state feedback and the output feedback regulator problem. In the latter case, the measurement from the Schrödinger equation is taken at the boundary. First we show that the open-loop system is well-posed. We design a state feedback control law that solves the regulator problem by the backstepping method. Then, a finite-dimensional reference observer and an infinitedimensional disturbance observer are designed. Putting these together, we obtain an output feedback controller with internal loop that achieves output regulation.2010 Mathematics Subject Classification. 34L40, 93B52, 93D15.

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Section: Properties Of the System To Be Controlledmentioning

confidence: 99%

Section: Introduction and Problem Formulationmentioning

confidence: 99%

The regulation problem for the one-dimensional Schrödinger equation via the backstepping approach

Zhou

2016

2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE)

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“…In control system, cascaded PDE-ODE and PDE-PDE systems describe fundamental laws of physics and mechanic, such as ODE-Schrödinger equation [1][2][3], ODE-Heat equation [4][5][6][7], ODE-Wave equation [6,8,9], coupled strings [10], coupled Timoshenko beam [11] etc. The stabilization of systems utilizing PDEs subject to time delay is drawn more attention [12][13][14][15][16][17].…”

Section: Motivation and Incitementmentioning

confidence: 99%

Output feedback stabilization of cascaded ODE‐Wave equations with time delay in observation

Than

Wang

2019

Asian Journal of Control

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In this paper, we are concerned with the stabilization of a cascaded ODE‐wave system subject to boundary observation with time delay. Well‐posedness of the open‐loop system is observable to show first. Both observer and predictor systems are designed to estimate the state variable on the time interval [0,t−τ] when the observation is available, and to predict the state variable on the time interval [t−τ,t] when the observation is not available respectively. Next, we transform the original system to the well‐posed and exponentially stable system by the backstepping method. Based on the estimated state variable and the output feedback stabilizing controller using the backstepping method. It is shown that the closed‐loop system is exponentially stable. The numerical simulation is presented to illustrate the effect of the stabilizing controller.

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“…In [2], the same problem is also studied for a wave with a general boundary disturbance by the disturbance treatment technique which is firstly proposed in [3]. These results were extended to regulate the output of a Schrödinger equation in [4,5]. However, the literature mentioned above is considered in a relative easy situation where the performance output is always collocated to the control actuation.…”

Section: Introductionmentioning

confidence: 99%

Performance Output Tracking for a One‐Dimensional Wave‐Heat Cascade System with Unmatched Disturbance

Liu

2019

Complexity

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The objective of this paper is to solve the performance output regulation problem for a wave-heat cascade system with unmatched disturbance. Applying the series expansion, the auxiliary trajectory for the cascade system is constructed and the unmatched disturbance is rejected. Meanwhile, the controller and observer only based on error signal are designed, and the performance output regulation problem is solved. Under the control feedback, the performance output can track the reference signal, and the regulation error goes to zero asymptotically. Finally, some numerical simulations are presented for illustration.

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Output Tracking for One‐Dimensional Schrödinger Equation subject to Boundary Disturbance

Cited by 11 publications

References 28 publications

The regulation problem for the one-dimensional Schrödinger equation via the backstepping approach

The regulation problem for the one-dimensional Schrödinger equation via the backstepping approach

Output feedback stabilization of cascaded ODE‐Wave equations with time delay in observation

Performance Output Tracking for a One‐Dimensional Wave‐Heat Cascade System with Unmatched Disturbance

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