Inexact Newton-Type Optimization with Iterated Sensitivities for Nonlinear Model Predictive Control of Cyclic Processes


Conrad Marquardt

Thursday, December 19, 2019, 9:30

Room 03-011, Georges-Köhler Allee 102, Freiburg 79110, Germany

The inexact Newton-type method with iterated sensitivities (INIS) is a Newton-type method suited for problems, where a subset of the variable is defined by a nonlinear equality constraint. These constraints are called the forward problem. The algorithm is applicable using any approximations of the Jacobian of the forward problem. In contrast to other inexact Newton (IN) methods, the INIS algorithm preserves the local convergence properties and the asymptotic contraction rate of the Newton-type scheme for the forward problem. There also exists an adjoint-free version (AF-INIS) of the method.

In this thesis we analysis the method for the open-loop Nonlinear Model Predictive Control (NMPC) of a cyclic-switched system arising from the cycle-to-cycle control of the gasoline controlled autoignition (GCAI) process of a low temperature combustion engines. The convergence properties of INIS and AF-INIS are compared with the convergence properties of the Newton-type scheme for the forward problem. The computational costs of one iteration of the INIS and AF-INIS are compared with the computational cost of one iteration the Gauss-Newton (GN) algorithm. Furthermore the efficiency, that is computational cost until convergence, of the INIS, AF-INIS, GN and an IN algorithms are compared. 

In addition, a version of the algorithm applicable for real-time iteration (RTI) for closed-loop problems was implemented and tested. Also further possibilities to use INIS in this context were discussed.