Adaptive Observer for a Class of Parabolic PDEs

Ahmed‐Ali, Tarek; Giri, F.; Krstić, Miroslav; Lamnabhi‐Lagarrigue, Françoise; Burlion, Laurent

doi:10.1109/tac.2015.2500237

Cited by 50 publications

(28 citation statements)

References 21 publications

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“…INTRODUCTION a) Control of parabolic PDEs: Parabolic partial differential equations (PDEs) are predominately used in describing fluid, thermal, and chemical dynamics, including many applications of sea ice melting and freezing [28], continuous casting of steel [20] and lithium-ion batteries [15]. These therefore give rise to related important control and estimation problems, i.e., the boundary control and state observation of parabolic PDEs in [11], [14], [6], [19], [5], [7], [8], [18] and [2], [22], [23] respectively. b) Control of parabolic PDE-ODE systems: In addition to the aforementioned works on parabolic PDEs, topics concerning parabolic PDE-ODE coupled systems are also popular, which have rich physical background such as coupled electromagnetic, coupled mechanical, and coupled chemical reactions [25].…”

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confidence: 99%

Output Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs

Wang

Krstić

2019

IEEE Trans. Automat. Contr.

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We present designs for exponential stabilization of an ODE-heat PDE-ODE coupled system where the control actuation only acts in one ODE. The combination of PDE backstepping and ODE backstepping is employed in a state-feedback control law and in an observer that estimates PDE and two ODE states only using one PDE boundary measurement. Based on the state-feedback control law and the observer, the outputfeedback control law is then proposed. The exponential stability of the closed-loop system and the boundedness and exponential convergence of the control law are proved via Lyapunov analysis. Finally, numerical simulations validate the effectiveness of this method for the "sandwiched" system.

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confidence: 99%

Output Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs

Wang

Krstić

2019

IEEE Trans. Automat. Contr.

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“…In this study, it is assumed that the switching signal is arbitrary subjects to ] ( ) = 1, 0 ( ∈ ), which means that the -th subsystem is active or not, respectively. Thus the fuzzy switched PDE system (7) can be inferred as follows:…”

Section: Preliminary System and T-s Fuzzy Modelmentioning

confidence: 99%

“…[1]. In the past decades, considerable research has been conducted for distributed parameter systems (DPSs), especially hyperbolic and parabolic PDE systems [2][3][4][5][6][7][8][9][10]. To mention a few, the authors in [2] investigated the state estimation problem of linear parabolic PDE systems via using backstepping technique, [3] considered the robust controller design for hyperbolic DPSs, adaptive control approach of parabolic PDE systems was proposed in [4][5][6], and [10] investigated boundary control problem of parabolic PDE systems with parameter variations.…”

Section: Introductionmentioning

confidence: 99%

Dissipativity‐Based Controller Design for Time‐Delayed T‐S Fuzzy Switched Distributed Parameter Systems

et al. 2018

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This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

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“…Recalling the above limitations, an adaptive relative velocity estimation (ARVE) algorithm is presented in the current article. Adaptive techniques have been already developed as controller methods as well as observer algorithms in diverse applications . Here, an adaptive technique is incorporated in a solution for problem of relative velocity estimation for aerial AMRs.…”

Section: Introductionmentioning

confidence: 99%

Adaptive relative velocity estimation algorithm for autonomous mobile robots using the measurements on acceleration and relative distance

Safaei

2020

Adaptive Control & Signal

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Summary In this article, an adaptive algorithm is proposed for online velocity estimation of the autonomous mobile robots (AMRs) without positioning data received from a Global Positioning System (GPS) module or other means for odometry. Unlike the popular Kalman and particle filters that use the measurements on vectors of global (or local) position and acceleration of a mobile robot, the proposed adaptive relative velocity estimation (ARVE) algorithm requires the scalar value of measured distance to a beacon agent and also the measurement on acceleration vector, in order to generate an online estimation of the global velocity vector of a mobile robot. Combining the ARVE algorithm with the recently proposed adaptive relative position estimation (ARPE) algorithm provides a solution for online estimation of the translational states of a mobile robot without accessing the GPS data, which makes the package applicable in both indoor and outdoor environments. The stability of the ARVE algorithm is analyzed with LaSalle‐Yoshizawa theorem. In addition, two simulation studies are provided to show the application of the proposed estimation package (ARVE+ARPE) for aerial AMRs in two cases corresponding to the stationary and moving beacon agents. In the simulation results, it is shown that the estimation package can be used in conjunction with the recently proposed adaptive model‐free control (AMFC) algorithm to achieve desired tracking objective in autonomous movement of a quadrotor, without requiring the information on the internal dynamics of the robot.

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Adaptive Observer for a Class of Parabolic PDEs

Cited by 50 publications

References 21 publications

Output Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs

Output Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs

Dissipativity‐Based Controller Design for Time‐Delayed T‐S Fuzzy Switched Distributed Parameter Systems

Adaptive relative velocity estimation algorithm for autonomous mobile robots using the measurements on acceleration and relative distance

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