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Minimax Sliding Mode Control Design for Linear Evolution Equations with Noisy Measurements and Uncertain Inputs

Sergiy Zhuk 1 Orest Iftime 2 Jonathan Epperlein 1 Andrey Polyakov 3
3 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : We extend a sliding mode control methodology to linear evolution equations with uncertain but bounded inputs and noise in observations. We first describe the reachability set of the state equation in the form of an infinite-dimensional ellipsoid, and then steer the minimax center of this ellipsoid toward a finitedimensional sliding surface in finite time by using the standard sliding mode output-feedback controller in equivalent form. We demonstrate that the designed controller is the best (in the minimax sense) in the class of all measurable functionals of the output. Our design is illustrated by two numerical examples: output-feedback stabilization of linear delay equations, and control of moments for an advection-diffusion equation in 2D.
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https://hal.inria.fr/hal-03083467
Contributor : Andrey Polyakov <>
Submitted on : Saturday, December 19, 2020 - 9:25:47 AM
Last modification on : Friday, January 22, 2021 - 3:06:09 PM

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Sergiy Zhuk, Orest Iftime, Jonathan Epperlein, Andrey Polyakov. Minimax Sliding Mode Control Design for Linear Evolution Equations with Noisy Measurements and Uncertain Inputs. Systems and Control Letters, Elsevier, In press, ⟨10.1016/j.sysconle.2020.104830⟩. ⟨hal-03083467⟩

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