We present a data-driven method to synthesize robust control invariant (RCI) sets for linear parameter-varying (LPV) systems subject to unknown but bounded disturbances. A finite-length data set consisting of state, input, and scheduling signal measurements is used to compute an RCI set and invariance-inducing controller, without identifying an LPV model of the system. We parameterize the RCI set as a configuration-constrained polytope whose facets have a fixed orientation and variable offset. This allows us to define the vertices of the polytopic set in terms of its offset. By exploiting this property, an RCI set and associated vertex control inputs are computed by solving a single linear programming (LP) problem, formulated based on a data-based invariance condition and system constraints. We illustrate the effectiveness of our approach via two numerical examples. The proposed method can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed. We show that RCI sets can be synthesized even with a relatively small number of data samples, if the gathered data satisfy certain excitation conditions. © 2017 IEEE.

Data-Driven Synthesis of Configuration-Constrained Robust Invariant Sets for Linear Parameter-Varying Systems

M. Mejari;S. K. Mulagaleti;A. Bemporad
2023-01-01

Abstract

We present a data-driven method to synthesize robust control invariant (RCI) sets for linear parameter-varying (LPV) systems subject to unknown but bounded disturbances. A finite-length data set consisting of state, input, and scheduling signal measurements is used to compute an RCI set and invariance-inducing controller, without identifying an LPV model of the system. We parameterize the RCI set as a configuration-constrained polytope whose facets have a fixed orientation and variable offset. This allows us to define the vertices of the polytopic set in terms of its offset. By exploiting this property, an RCI set and associated vertex control inputs are computed by solving a single linear programming (LP) problem, formulated based on a data-based invariance condition and system constraints. We illustrate the effectiveness of our approach via two numerical examples. The proposed method can generate RCI sets that are of comparable size to those obtained by a model-based method in which exact knowledge of the system matrices is assumed. We show that RCI sets can be synthesized even with a relatively small number of data samples, if the gathered data satisfy certain excitation conditions. © 2017 IEEE.
2023
Constrained control
data driven control
linear parameter-varying systems
robust control
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/27898
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