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On the use of mixed‐integer linear programming for predictive control with avoidance constraints
Author(s) -
Maia Marcelo H.,
Galvão Roberto K. H.
Publication year - 2008
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1341
Subject(s) - model predictive control , obstacle avoidance , integer programming , mathematical optimization , control (management) , linear programming , computer science , regular polygon , sampling (signal processing) , control theory (sociology) , computation , integer (computer science) , mathematics , algorithm , artificial intelligence , geometry , filter (signal processing) , robot , programming language , computer vision , mobile robot
Abstract This technical note concerns the predictive control of discrete‐time linear models subject to state, input and avoidance polyhedral constraints. Owing to the presence of avoidance constraints, the optimization associated with the predictive control law is non‐convex, even though the constraints themselves are convex. The inclusion of the avoidance constraints in the predictive control law is achieved by the use of a modified version of a mixed‐integer programming approach previously derived in the literature. The proposed modification consists of adding constraints to ensure that linear segments of the system trajectories between consecutive sampling times do not cross existing obstacles. This avoids the significant extra computation that would be incurred if the sampling time was reduced to prevent these crossings. Simulation results show that the inclusion of these additional constraints successfully prevents obstacle collisions that would otherwise occur. Copyright © 2008 John Wiley & Sons, Ltd.