Robust Updated MPC Schemes

by Vryan Gil Palma

Institution: Universität Bayreuth
Department: Mathematik, Physik und Informatik
Degree: PhD
Year: 2015
Record ID: 1100380
Full text PDF: https://epub.uni-bayreuth.de/2056/


We consider model predictive control (MPC) approaches to approximate the solution of infinite horizon optimal control problems (OCPs) for perturbed nonlinear discrete time systems. MPC provides an algorithmic synthesis of an approximately optimal feedback law by iteratively solving finite horizon OCPs. The optimization problem to be solved at each time step results in a high computational expense and computational latency. As computationally costly MPC controllers may demand implementation on highly powerful computing systems to meet real-time requirements, we address the challenge of developing algorithms that are less computationally demanding without sacrificing the control performance to cater to systems with fast dynamics. In using the multistep MPC strategy, we reduce the number of optimizations to be performed hence considerably lowering the computational load. However, this approach comes with the disadvantage of reduced robustness of the closed-loop solution against perturbations. We introduce the updated multistep MPC where an update is performed to the multistep MPC based on re-optimizations on shrinking horizons giving a straightforward approach to provide a coping mechanism to counteract the perturbations. Robust performance improvements due to re-optimization are rigorously quantified. This is achieved by analyzing the open-loop control strategy and the shrinking horizon strategy on finite horizon OCPs for systems under perturbations where potential performance improvement brought about by the re-optimization is quantified. This analysis of potential benefits extends to the setting where the moving horizon MPC strategy is used for the infinite horizon setting. Lastly, we consider the sensitivity-based multistep MPC which is a particular MPC variant that allows further savings in computational load by using sensitivity analysis. The sensitivities used to update the multistep MPC can be computed efficiently by exploiting the matrix structures resulting from the MPC problem formulation. For this scheme, we show that the sensitivity-based control is a linear approximation of the re-optimization-based control and therefore, the analysis on the performance and stability properties of the updated multistep MPC can be carried over to the sensitivity-based multistep MPC. We compare the MPC schemes and confirm our theoretical results through numerical examples. We also examine the control performance and computing complexity requirements of the schemes and analyze their potential and suitability to be implemented on embedded systems with limited computing power. Wir untersuchen Modellprädiktive Regelungsalgorithmen (MPC Algorithmen) zur Approximation von Optimalsteuerungsproblemen (OCPs) auf unendlichem Zeithorizont für gestörte nichtlineare diskrete dynamische Systeme. MPC liefert ein approximativ optimales Feedback durch die iterative Lösung von OCPs auf endlichem Zeithorizont. Das in jedem Zeitschritt zu lösende Optimierungsproblem ist sehr rechenaufwändig und führt zu Verzögerungen. Der…