scholarly journals Region of attraction analysis via invariant sets

2014 ◽  
Author(s):  
Giorgio Valmorbida ◽  
James Anderson
Keyword(s):  
Invariant Sets ◽  
Region Of Attraction

scholarly journals Robust estimations of the Region of Attraction using invariant sets

2019 ◽  
Vol 356 (8) ◽  
pp. 4622-4647 ◽  
Author(s):  
Andrea Iannelli ◽  
Andrés Marcos ◽  
Mark Lowenberg
Keyword(s):  
Invariant Sets ◽  
Region Of Attraction

scholarly journals A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2087
Author(s):  
Ismi Rosyiana Fitri ◽  
Jung-Su Kim
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Convex Combination ◽  
Invariant Sets ◽  
Region Of Attraction ◽  
Control Laws ◽  
Terminal Set ◽  
The One ◽  
The Given ◽  
Regions Of Attraction

In the dual-mode model predictive control (MPC) framework, the size of the stabilizable set, which is also the region of attraction, depends on the terminal constraint set. This paper aims to formulate a larger terminal set for enlarging the region of attraction in a nonlinear MPC. Given several control laws and their corresponding terminal invariant sets, a convex combination of the given sets is used to construct a time-varying terminal set. The resulting region of attraction is the union of the regions of attraction from each invariant set. Simulation results show that the proposed MPC has a larger stabilizable initial set than the one obtained when a fixed terminal set is used.

scholarly journals Estimating the region of attraction of uncertain systems with invariant sets

2018 ◽  
Vol 51 (25) ◽  
pp. 246-251
Author(s):  
A. Iannelli ◽  
A. Marcos ◽  
M. Lowenberg
Keyword(s):  
Uncertain Systems ◽  
Invariant Sets ◽  
Region Of Attraction

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

Sign in / Sign up

Export Citation Format

Share Document