Robust Quadratic-Optimal Control of TS-Fuzzy-Model-Based Dynamic Systems With Both Elemental Parametric Uncertainties and Norm-Bounded Approximation Error

This paper considers the design problem of the robust quadratic-optimal parallel-distributed-compensation (PDC) controllers for Takagi-Sugeno (TS) fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error. By complementarily fusing the robust...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems Vol. 17; no. 3; pp. 518 - 531
Main Authors: Ho, Wen-Hsien, Tsai, Jinn-Tsong, Chou, Jyh-Horng
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2009
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Approximation error
Control systems
Controllers
Design engineering
Dynamical systems
Dynamics
Errors
Genetic algorithms
Hybrid Taguchi-genetic algorithm (HTGA)
Linear matrix inequalities
linear matrix inequalities (LMIs)
Mathematical analysis
orthogonal functions approach (OFA)
Performance analysis
quadratic-optimal control
Robust control
robust stabilizability
Robustness
Studies
Takagi-Sugeno (TS) fuzzy model
Takagi-Sugeno model
Uncertainty
Takagi-Sugeno fuzzy model
hybrid Taguchi-genetic algorithm
quadratic optimal control
robust stabilizability
orthogonal-funcations approach
linear matrix inequalities
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary:This paper considers the design problem of the robust quadratic-optimal parallel-distributed-compensation (PDC) controllers for Takagi-Sugeno (TS) fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error. By complementarily fusing the robust stabilizability condition, the orthogonal functions approach (OFA), and the hybrid Taguchi genetic algorithm (HTGA), an integrative method is presented in this paper to design the robust quadratic-optimal PDC controllers such that 1) the uncertain TS-fuzzy-model-based control systems can be robustly stabilized, and 2) a quadratic integral performance index for the nominal TS-fuzzy-model-based control systems can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). By using the OFA and the LMI-based robust stabilizability condition, the robust quadratic-optimal PDC control problem for the uncertain TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition, thus greatly simplifying the robust optimal PDC control design problem. Then, for the static constrained-optimization problem, the HTGA is employed to find the robust quadratic-optimal PDC controllers of the uncertain TS-fuzzy-model-based control systems. Two design examples of the robust quadratic-optimal PDC controllers for an uncertain inverted pendulum system and an uncertain nonlinear mass-spring-damper mechanical system are given to demonstrate the applicability of the proposed integrative approach.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2008.924220