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Volume 5 Issue 4
Jul.  2018

IEEE/CAA Journal of Automatica Sinica

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Lantao Xie, Lei Xie, Hongye Su and Jingdai Wang, "Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 765-770, July 2018. doi: 10.1109/JAS.2018.7511126
Citation: Lantao Xie, Lei Xie, Hongye Su and Jingdai Wang, "Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems," IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 765-770, July 2018. doi: 10.1109/JAS.2018.7511126

Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems

doi: 10.1109/JAS.2018.7511126

the Natural Science Foundation of Zhejiang Province LR17F030002

the Science Fund for Creative Research Groups of the National Natural Science Foundation of China 61621002

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  • Feasible sets play an important role in model predictive control (MPC) optimal control problems (OCPs). This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both spectrahedron (represented by linear matrix inequalities) and polyhedral (represented by a set of inequalities) 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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