Robust hybrid predictive control of nonlinear systems
type: Item
instance of: scholarly article
title: Robust hybrid predictive control of nonlinear systems
zbMATH Open document ID: 1089.93009
author: Prashant Mhaskar
author: Nael H. El-Farra
author: Panagiotis D. Christofides
published in: Automatica
publication date: 2005-02-23T00:00:00Z
review text: The paper considers nonlinear systems with uncertain variables and input constraints, described by \[ \dot x=f(x)+G(x)u+W(x)\theta(t), \quad x\in\mathbb R^n, \quad u\in\mathbf U\subset\mathbb R^m,\quad \theta(t)\in\Theta\subset\mathbb R^k, \tag{1} \] where \(x\) is the vector of state variables, \(u\) is the vector of constrained manipulated inputs, \(\theta(t)\) is the vector of uncertain bounded variables and \(f(0)=0\). The vector function \(f(x)\) and the matrices \(G(x)\) and \(W(x)\) are assumed to be sufficiently smooth. For the system (1), the paper presents a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The approach uses a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained. Thus, a stability region within which any available MPC formulation can be implemented is provided. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event the predictive controller fails to yield a control move or leads to instability. As an example, the implementation of the robust hybrid predictive control structure is demonstrated by simulations of a chemical process.
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 2137842
zbMATH Keywords: input constraints
zbMATH Keywords: Lyapunov-based bounded control
zbMATH Keywords: model predictive control
zbMATH Keywords: controller switching
zbMATH Keywords: hybrid systems
zbMATH Keywords: stability region
MaRDI profile type: Publication
full work available at URL: j.automatica.2004.08.020
OpenAlex ID: W2155499191
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DOI: 10.1016/J.AUTOMATICA.2004.08.020
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description: scientific article; zbMATH DE number 2137842