Polyhedral feasible set computation of MPC-based optimal control problems

Feasible sets play an important role in model predictive control &#x0028 MPC &#x0029 optimal control problems &#x0028 OCPs &#x0029. This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both...

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Bibliographic Details
Published in:IEEE/CAA journal of automatica sinica Vol. 5; no. 4; pp. 765 - 770
Main Authors: Xie, Lantao, Xie, Lei, Su, Hongye, Wang, Jingdai
Format: Journal Article
Language:English
Published: Piscataway Chinese Association of Automation (CAA) 01.07.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Computer simulation
Energy consumption
Linear matrix inequalities
Mathematical analysis
Matrix methods
Optimal control
Parametric statistics
Predictive control
Spherical coordinates
ISSN:2329-9266, 2329-9274
Online Access:Get full text
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Summary:Feasible sets play an important role in model predictive control &#x0028 MPC &#x0029 optimal control problems &#x0028 OCPs &#x0029. This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both spectrahedron &#x0028 represented by linear matrix inequalities &#x0029 and polyhedral &#x0028 represented by a set of inequalities &#x0029 constraints. According to the geometrical meaning of the inner product of vectors, the maximum length of the projection vector from the feasible set to a unit spherical coordinates vector is computed and the optimal solution has been proved to be one of the vertices of the feasible set. After computing the vertices, the convex hull of these vertices is determined which equals the feasible set. The simulation results show that the proposed method is especially efficient for low dimensional feasible set computation and avoids the non-unicity problem of optimizers as well as the memory consumption problem that encountered by projection algorithms.
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ISSN:2329-9266
2329-9274
DOI:10.1109/JAS.2018.7511126