Guaranteed cost control of affine nonlinear systems via partition of unity method

We consider the problem of guaranteed cost control (GCC) of affine nonlinear systems in this paper. Firstly, the general affine nonlinear system with the origin being its equilibrium point is represented as a linear-like structure with state-dependent coefficient matrices. Secondly, partition of uni...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 49; no. 2; pp. 660 - 666
Main Authors: Han, Dongfang, Shi, Ling
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.02.2013
Elsevier
Subjects:
Affine nonlinear systems
Applied sciences
Computer science; control theory; systems
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Dynamical systems
Errors
Exact sciences and technology
Guaranteed cost control (GCC)
Law
Linear matrix inequality (LMI)
Mathematical analysis
Mathematical models
Matrices
Nonlinear dynamics
Optimal control
Linear matrix inequality (LMI)
Guaranteed cost control (GCC)
Affine nonlinear systems
Control program
Non linear control
Control synthesis
Modeling
Asymptotic stability
Linear matrix inequality
Cost function
Optimal control (mathematics)
Mathematical programming
Systeme affine in control
Nonlinear problems
Non linear system
Affine transformation
Equilibrium point
Upper bound
Equations of state
Hamilton Jacobi equation
Optimal control
Problem solving
State dependence
Riccati equation
Unity partition
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:We consider the problem of guaranteed cost control (GCC) of affine nonlinear systems in this paper. Firstly, the general affine nonlinear system with the origin being its equilibrium point is represented as a linear-like structure with state-dependent coefficient matrices. Secondly, partition of unity method is used to approximate the coefficient matrices, as a result of which the original affine nonlinear system is equivalently converted into a linear-like system with modeling error. A GCC law is then synthesized based on the equivalent model in the presence of modeling error under certain error condition. The control law ensures that the system under control is asymptotically stable as well as that a given cost function is upper-bounded. A suboptimal GCC law can be obtained via solving an optimization problem in terms of linear matrix inequality (LMI), in stead of state-dependent Riccati equation (SDRE) or Hamilton–Jacobi equations that are usually required in solving nonlinear optimal control problems. Finally, a numerical example is provided to illustrate the validity of the proposed method.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2012.11.050