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Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems
Author(s) -
Chen QiuXia,
He DeFeng,
Yu Li
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.314
Subject(s) - control theory (sociology) , linear matrix inequality , nonlinear system , robustness (evolution) , convex optimization , bounded function , stability (learning theory) , mathematics , model predictive control , state (computer science) , mathematical optimization , computer science , regular polygon , control (management) , algorithm , mathematical analysis , biochemistry , chemistry , physics , geometry , quantum mechanics , artificial intelligence , machine learning , gene
This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time‐varying delay systems subject to bounded disturbances. The notion of the input‐to‐state stability (ISS) of nonlinear time‐delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay‐dependent sufficient condition is derived to guarantee input‐to‐state practical stability (ISpS) of the closed‐loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non‐convex min‐max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck‐trailer is used to illustrate the effectiveness of the proposed results.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society