Backstepping observer design for parabolic PDEs with measurement of weighted spatial averages

Tsubakino, Daisuke; Hara, Shinji

doi:10.1016/j.automatica.2014.12.019

Cited by 26 publications

(12 citation statements)

References 23 publications

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“…is the real vector regulator and the output Y out (t) is a vector collecting the weighted average of the state over the entire spatial domain [27]…”

Section: Introductionmentioning

confidence: 99%

Output regulation of anti‐stable coupled wave equations via the backstepping technique

Wang

Guo

2018

IET Control Theory & Applications

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This study is concerned with the output regulation of an anti-stable system of coupled wave equations with external disturbances. A state-feedback regulator is designed to force the output of the coupled wave equations to track the reference signal, which is generated by an exosystem. Moreover, the tracking error decays exponentially at a prescribed rate. The design is based on backstepping approach and relies on solving the regulator equations. The solvability condition of the regulator equations is characterised by the transfer matrix of the coupled wave equations and eigenvalues of the exosystem. An outputfeedback regulator is then constructed by developing an observer. Finally, the numerical simulations are demonstrated for the effectiveness of the theoretical results.

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“…is the real vector regulator and the output Y out (t) is a vector collecting the weighted average of the state over the entire spatial domain [27]…”

Section: Introductionmentioning

confidence: 99%

Output regulation of anti‐stable coupled wave equations via the backstepping technique

Wang

Guo

2018

IET Control Theory & Applications

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“…For instance, naturally, in dynamics with non-local terms involving the whole spatial domain, in PDE models [25] or in finite-dimensional systems with distributed delays [29]. Additionally, in design-oriented problems such as: control of coupled PDE-ODE (Ordinary Differential Equations) systems by under-actuated schemes [27], [28] (fewer actuators than spatial states [30]; it avoids an additional control action to cancel the non-strict feedback term [20]), or observer design for systems the output of which (sensing) comprises the states on the whole domain [31]. In these cases, a Volterra-type transformation cannot be used (at least directly) and the application of a Fredholm-type transformation leads to new and intricate mathematical problems (operator invertibility, Kernel solvability) [30].…”

Section: Introductionmentioning

confidence: 99%

Backstepping PDE Design: A Convex Optimization Approach

Ascencio

Astolfi

Parisini

2018

IEEE Trans. Automat. Contr.

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Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sumof-Squares (SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L 2-norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs.

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“…Based on these techniques, the reference planning and tracking control strategies have been proposed for parabolic systems within a higher‐dimensional domain, also. Furthermore, the backstepping method has been derived to design the observer in one‐dimensional or high‐dimensional cases, such as Smyshlyaev and Krstic, Jadachowski et al, and Tsubakino and Hara . More recently, motivated by backstepping techniques on infinite dimensional systems, the boundary control problem for nonlinear parabolic PDEs has achieved a great progress.…”

Section: Introductionmentioning

confidence: 99%

Boundary output feedback stabilization for a class of coupled parabolic systems

2017

Math Methods in App Sciences

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In this paper, the boundary output feedback stabilization problem is addressed for a class of coupled nonlinear parabolic systems. An output feedback controller is presented by introducing a Luenberger-type observer based on the measured outputs.To determine observer gains, a backstepping transform is introduced by choosing a suitable target system with nonlinearity. Furthermore, based on the state observer, a backstepping boundary control scheme is presented. With rigorous analysis, it is proved that the states of nonlinear closed-loop system including state estimation and estimation error of plant system are locally exponentially stable in the L 2 norm. Finally, a numerical example is proposed to illustrate the effectiveness of the presented scheme. KEYWORDSbackstepping, boundary control, locally exponentially stable, output feedback 6510

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Backstepping observer design for parabolic PDEs with measurement of weighted spatial averages

Cited by 26 publications

References 23 publications

Output regulation of anti‐stable coupled wave equations via the backstepping technique

Output regulation of anti‐stable coupled wave equations via the backstepping technique

Backstepping PDE Design: A Convex Optimization Approach

Boundary output feedback stabilization for a class of coupled parabolic systems

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