Open AccessComputationally efficient model predictive control for a class of linear parameter‐varying systems
Author(s) -
Cavanini Luca,
Cimini Gionata,
Ippoliti Gianluca
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.1096
Subject(s) - model predictive control , invertible matrix , control theory (sociology) , computer science , computational complexity theory , linear system , transformation (genetics) , quadratic programming , linear programming , dimension (graph theory) , quadratic equation , linear dynamical system , matrix (chemical analysis) , transformation matrix , coordinate system , mathematical optimization , control (management) , algorithm , mathematics , artificial intelligence , mathematical analysis , biochemistry , chemistry , materials science , geometry , kinematics , physics , classical mechanics , pure mathematics , composite material , gene
The use of linear parameter varying (LPV) prediction models has been proven to be an effective solution to develop model predictive control (MPC) algorithms for linear and non‐linear systems. However, the computational effort is a crucial issue for LPV‐MPC, which has severely limited its application especially in embedded control. Indeed, for dynamical systems of dimension commonly found in embedded applications, the time needed to form the quadratic programming (QP) problem at each time step, can be substantially higher than the average time to solve it, making the approach infeasible in many control boards. This study presents an algorithm that drastically reduces this computational complexity for a particular class of LPV systems. They show that when the input matrix is right‐invertible, the rebuild phase of the QP problem can be accelerated by means of a coordinate transformation which approximates the original formulation. Then they introduce a variant of the algorithm, able to further reduce this time, at the cost of a slightly increased sub‐optimality. The presented results on vehicle dynamics and electrical motor control confirm the effectiveness of the two novel methods, especially in those applications where computational load is a key indicator for success.