Sparse preconditioning for model predictive control

We propose fast O(N) preconditioning, where N is the number of gridpoints on the prediction horizon, for iterative solution of (non)-linear systems appearing in model predictive control methods such as forward-difference Newton-Krylov methods. The Continuation/GMRES method for nonlinear model predictive control, suggested by T. Ohtsuka in 2004, is a specific application of the Newton-Krylov method, which uses the GMRES iterative algorithm to solve a forward difference approximation of the optimality equations on every time step.Comment: 6 pages, 5 figures, to appear in proceedings of the American Control Conference 2016, July 6-8, Boston, MA, USA. arXiv admin note: text overlap with arXiv:1509.0286

Continuation methods and disjoint equilibria

International audienceContinuation methods are efficient to trace branches of fixed point solutions in parameter space as long as these branches are connected. However, the computation of isolated branches of fixed points is a crucial issue and require ad-hoc techniques. We suggest a modification of the standard continuation methods to determine these isolated branches more systematically. The so-called residue continuation method is a global homotopy starting from an arbitrary disjoint initial guess. Explicit conditions ensuring the quadratic convergence of the underlying Newton-Raphson process are derived and illustrated through several examples

Newton-Picard Gauss-Seidel

Newton-Picard methods are iterative methods that work well for computing roots of nonlinear equations within a continuation framework. This project presents one of these methods and includes the results of a computation involving the Brusselator problem performed by an implementation of the method. This work was done in collaboration with Andrew Salinger at Sandia National Laboratories