Globally Optimal Nonlinear Model Predictive Control

Abstract This paper presents a globally optimal nonlinear Model Predictive Control (NMPC) algorithm. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions. In complex problems, local solver reliability is difficult to predict and often highly dependent upon the choice of initial guess. For the purpose of NMPC, local solvers can cause unexpected closed-loop results or failure of the algorithm. Stochastic attempts at global optimization of NMPC methods cannot provide rigorous bounds on the optimality of the resulting solution. Implementation of a global solution technique (Falk and Soland [1969], Horst and Tuy [1990]), which guarantees global optimality, restores the integrity of NMPC technology. Due to the combinatorial nature of nonconvex optimization, real-time considerations must be considered. The proposed algorithm's capabilities are demonstrated by the application of the controller on the benchmark control problem of the isothermal operation of a continuous stirred tank reactor (CSTR) with Van de Vusse reactions (Kremling and Allgower [1993]).

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