# American Institute of Mathematical Sciences

September  2015, 35(9): 4385-4414. doi: 10.3934/dcds.2015.35.4385

## Robustness of performance and stability for multistep and updated multistep MPC schemes

 1 University of Bayreuth, Chair of Applied Mathematics, Universitätsstraße 30, 95440 Bayreuth, Germany, Germany

Received  May 2014 Revised  August 2014 Published  April 2015

We consider a model predictive control approach to approximate the solution of infinite horizon optimal control problems for perturbed nonlinear discrete time systems. By reducing the number of re-optimizations, the computational load can be lowered considerably at the expense of reduced robustness of the closed-loop solution against perturbations. In this paper, we propose and analyze an update strategy based on re-optimizations on shrinking horizons which is computationally less expensive than that based on full horizon re-optimization, and at the same time allowing for rigorously quantifiable robust performance estimates.
Citation: Lars Grüne, Vryan Gil Palma. Robustness of performance and stability for multistep and updated multistep MPC schemes. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4385-4414. doi: 10.3934/dcds.2015.35.4385
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