A Primal Active-Set Minimal-Representation Algorithm for Polytopes with Application to Invariant-Set Calculations

Klintberg, Emil; Nilsson, Magnus; Mårdh, Lars Johannesson; Gupta, Ankit

doi:10.1109/cdc.2018.8619642

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…If all inequalities describing a polyhedron are necessary, we have a minimal-representation of the polyhedron. An approach that describes how to find the minimal-representation of the polyhedron is presented in [17] and is used in this paper.…”

Section: A Polytopes and Redundant Inequalitiesmentioning

confidence: 99%

A safety monitoring concept for fully automated driving

Kojchev

Klintberg

Fredriksson

2020

2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC)

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Safe motion planning for automated vehicles requires that a collision-free trajectory can be guaranteed. For that purpose, we propose a monitoring concept that would ensure safe vehicle states. Determining these safe states, however, is usually a computationally demanding task. To alleviate the computational demand, we investigate the possibility to compute the safe sets offline. To achieve this, we leverage backward reachability theory and compute the N-step robust backward reachable set offline. Based on the current disturbances, we demonstrate the possibility to adapt this set online. The safety guarantees are then provided by computing the robust one-step forward prediction of the state vector and checking if these states are members of the adapted safe set. The numerical example demonstrates that the approach is capable of avoiding hazardous vehicle states under an unsafe motion planning algorithm.

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Section: A Polytopes and Redundant Inequalitiesmentioning

confidence: 99%

A safety monitoring concept for fully automated driving

Kojchev

Klintberg

Fredriksson

2020

2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC)

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“…In addition, the method presented in [14] may fail to find all prime representations of a face. A minimal representation of a polytope considered in Klintberg et al [8] is a representation of this polytope containing no redundant constraints. Therefore, it can happen that a minimal representation of a polytope considered in their work is not a minimal representation in the sense of [16].…”

Section: Introductionmentioning

confidence: 99%

Minimal Representations of a Face of a Convex Polyhedron and Some Applications

2021

Acta Math Vietnam

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In this paper, we propose a method for determining all minimal representations of a face of a polyhedron defined by a system of linear inequalities. Main difficulties for determining prime and minimal representations of a face are that the deletion of one redundant constraint can change the redundancy of other constraints and the number of descriptor index pairs for the face can be huge. To reduce computational efforts in finding all minimal representations of a face, we prove and use properties that deleting strongly redundant constraints does not change the redundancy of other constraints and all minimal representations of a face can be found only in the set of all prime representations of the face corresponding to the maximal descriptor index set for it. The proposed method is based on a top-down search strategy, is easy to implement, and has many computational advantages. Based on minimal representations of a face, a reduction of degeneracy degrees of the face and ideas to improve some known methods for finding all maximal efficient faces in multiple objective linear programming are presented. Numerical examples are given to illustrate the method.

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“…A widely used algorithm to compute an RCI set for a linear system belongs to the class of the so‐called geometric approach, in which a recursive method based on one‐step backward reach operator is employed until some termination condition is matched. In each backward reach operation, numerical procedures like Minkowski sum, projection and finding minimal set representation are performed on polytopes, which can be computationally very demanding 1,7 . Depending upon the choice of the initial set, the result of such a recursive method is the arbitrarily close outer/inner approximation of the maximal RCI set 8,9 .…”

Section: Introductionmentioning

confidence: 99%

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

Gupta

Köroğlu

Falcone

2020

Intl J Robust & Nonlinear

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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.

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A Primal Active-Set Minimal-Representation Algorithm for Polytopes with Application to Invariant-Set Calculations

Cited by 4 publications

References 17 publications

A safety monitoring concept for fully automated driving

A safety monitoring concept for fully automated driving

Minimal Representations of a Face of a Convex Polyhedron and Some Applications

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

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