Computation of robust control invariant sets with predefined complexity for uncertain systems

Ankit Gupta; Hakan Köroğlu; Paolo Falcone

doi:10.1002/rnc.5378

Computation of robust control invariant sets with predefined complexity for uncertain systems

Ankit Gupta^*, Hakan Köroğlu, Paolo Falcone

^*Corresponding author for this work

Applied Mechanics

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Abstract

This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.

Original language	English
Pages (from-to)	1674-1688
Number of pages	15
Journal	International journal of robust and nonlinear control
Volume	31
Issue number	5
DOIs	https://doi.org/10.1002/rnc.5378
Publication status	Published - 25 Mar 2021

Keywords

invariant set
linear fractional transformation
linear matrix inequalities
linear systems
semi-definite program

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AU - Gupta, Ankit

AU - Köroğlu, Hakan

AU - Falcone, Paolo

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N2 - This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.

AB - This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.

KW - invariant set

KW - linear fractional transformation

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KW - semi-definite program

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Computation of robust control invariant sets with predefined complexity for uncertain systems

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