Backstepping-based extended Luenberger observer design for a Burgers-type PDE for multi-agent deployment

Freudenthaler, Gerhard; Göttsch, F.; Meurer, Thomas

doi:10.1016/j.ifacol.2017.08.1196

Cited by 7 publications

(1 citation statement)

References 10 publications

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“…[17] has also investigated observer designs where measurements are not given at a boundary, rather, as a weighted average (the state appearing underneath a bounded integral operator). A related result is [11], in which the authors consider the combination of boundary measurements with a single interior measurement to achieve estimation convergence for semilinear parabolic problems.…”

Section: Introductionmentioning

confidence: 99%

Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE

Chen

Vázquez

Krstić

2022

IEEE Trans. Automat. Contr.

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We present a novel methodology for designing output-feedback backstepping boundary controllers for an unstable 1-D diffusion-reaction partial differential equation with spatially-varying reaction. Using "folding transforms" the parabolic PDE into a 2 × 2 coupled parabolic PDE system with coupling via folding boundary conditions. The folding approach is novel in the sense that the design of bilateral controllers are generalized to center around arbitrary points, which become additional design parameters that can be separately chosen for the state-feedback controller and the state observer. The design can be selectively biased to achieve different performance indicies (e.g. energy, boundedness, etc). A first backstepping transformation is designed to map the unstable system into a strictfeedback intermediate target system. A second backstepping transformation is designed to stabilize the intermediate target system. The invertibility of the two transformations guarantees that the derived state-feedback controllers exponentially stabilize the trivial solution of the parabolic PDE system in the L 2 norm sense. A complementary state observer is likewise designed for the dual problem, where two collocated measurements are considered at an arbitrary point in the interior of the domain. The observer generates state estimates which converge to the true state exponentially fast in the L 2 sense. Finally, the output feedback control law is formulated by composing the statefeedback controller with the state estimates from the observer, and the resulting dynamic feedback is shown to stabilize the trivial solution of the interconnected system in the L 2 norm sense. Some analysis on how the selection of these points affect the responses of the controller and observer are discussed, with simulations illustrating various choices of folding points and their effect on the stabilization.

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Section: Introductionmentioning

confidence: 99%

Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE

Chen

Vázquez

Krstić

2022

IEEE Trans. Automat. Contr.

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PDE-based multi-agent formation control using flatness and backstepping: Analysis, design and robot experiments

Freudenthaler

Meurer

2020

Automatica

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A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling structure parameter information can be distributed within the agent continuum. Flatness-based motion planning and feedforward control are combined with a backstepping-based boundary controller to stabilise the distributed parameter system of the tracking error. The tracking controller utilises the required state information from a Luenberger-type state observer. By means of an exogenous system the relocation of formation profiles is achieved. The transfer of the control strategy to a finite-dimensional discrete multi-agent system is obtained by a suitable finite difference discretization of the continuum model, which in addition imposes a leader-follower communication topology. The results are evaluated both in simulation studies and in experiments for a swarm of mobile robots realizing the transition between different stable and unstable formation profiles.

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Bilateral backstepping control of coupled linear parabolic PDEs with spatially varying coefficients

Kerschbaum

Deutscher

2022

Automatica

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Backstepping-based extended Luenberger observer design for a Burgers-type PDE for multi-agent deployment

Cited by 7 publications

References 10 publications

Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE

Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE

PDE-based multi-agent formation control using flatness and backstepping: Analysis, design and robot experiments

Bilateral backstepping control of coupled linear parabolic PDEs with spatially varying coefficients

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