Nonlinear model predictive control with polytopic invariant sets.
type: Item
instance of: scholarly article
title: Nonlinear model predictive control with polytopic invariant sets.
zbMATH Open document ID: 1033.93022
DOI: 10.1016/S0005-1098(03)00128-6
author: Basil Kouvaritakis
author: Mark Cannon
author: Venkatesh Deshmukh
published in: Automatica
publication date: 2003-10-14T00:00:00Z
review text: A nonlinear model predictive control (NMPC) method in which low complexity polytopic invariant sets are used in place of ellipsoidal invariant sets is proposed. It is shown that (i) low-complexity polytopic invariant sets have larger volume than invariant ellipsoidal sets; (ii) the systematic design of maximum volume low-complexity invariant polytopes and linear feedback laws satisfying given performance bounds can be performed through the sequential off-line solution of a number of simple linear programs; and (iii) low-complexity invariant polytopic sets can be effectively used in NMPC of fast-sampling input-affine nonlinear systems. The advantages of feasible invariant polytopic sets over ellipsoidal sets are illustrated through the numerical examples. Also, the closed-loop performance of NMPC based on polytopic target sets is compared to NMPC based on ellipsoidal target sets.
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 1992652
zbMATH Keywords: polytopic invariant sets
zbMATH Keywords: nonlinear model predictive control
zbMATH Keywords: ellipsoidal invariant sets
zbMATH Keywords: linear feedback
zbMATH Keywords: linear programs
zbMATH Keywords: polytopic target sets
reviewed by: Ingmar Randvee
MaRDI profile type: Publication
cites work: Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions
cites work: Linear Matrix Inequalities in System and Control Theory
cites work: Open-loop and closed-loop optimality in interpolation MPC
cites work: A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability
cites work: Stabilizing receding-horizon control of nonlinear time-varying systems
cites work: Robust constrained model predictive control using linear matrix inequalities
cites work: A stabilizing model-based predictive control algorithm for nonlinear systems
cites work: Robust receding horizon control of constrained nonlinear systems
full work available at URL: s0005-1098(03)00128-6
OpenAlex ID: W2032155434
description: scientific article; zbMATH DE number 1992652