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Deterministic global optimization for nonlinear model predictive control of hybrid dynamic systems
Author(s) -
Long Christopher E.,
Polisetty Pradeep K.,
Gatzke Edward P.
Publication year - 2006
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.1105
Subject(s) - model predictive control , nonlinear system , mathematical optimization , robustness (evolution) , control theory (sociology) , computer science , stability (learning theory) , convergence (economics) , optimization problem , mathematics , control (management) , biochemistry , chemistry , physics , quantum mechanics , artificial intelligence , machine learning , economics , gene , economic growth
This paper applies a deterministic non‐convex optimization method for nonlinear model predictive control (NMPC) of systems exhibiting nonlinear hybrid dynamics. The process is represented by a model that incorporates nonlinearity using both continuous state variables and binary variables that define the multiple regimes of operation. The resulting optimization problem is a mixed‐integer nonlinear program (MINLP). A deterministic method is employed to provide rigorous bounds on the solution. In some cases, this method can guarantee global optimality of the non‐convex MINLP. Novel algorithm modifications are presented to improve convergence rates for the deterministic algorithm. The control algorithm is demonstrated using a simulated system of pressure tanks in which the volumetric flow through the process valves switches between distinct flow regimes. Terminal constraints and regime boundary constraints are imposed to promote stability and improve robustness. Formulation limitations and alternatives are discussed to address instances in which the resulting MINLP cannot be solved rapidly enough for real‐time implementation. This work shows that deterministic methods can be applied to NMPC applications while taking stability and uncertainty into account. Copyright © 2006 John Wiley & Sons, Ltd.