Constrained fuzzy controller design of discrete Takagi-Sugeno fuzzy models. (English) Zbl 1051.93057
The contribution of this paper is to provide a method in the design of a discrete fuzzy controller with linear output feedback gains for the discrete-time Takagi-Sugeno fuzzy systems. This method is based on the concept of the PDC (parallel distributed compensation) and it is developed according to a specified common observability Gramian, which can meet system performance requirements such as energy constraints and robust constraints. In the PDC approach, each control rule is designed from a corresponding rule of a Takagi-Sugeno fuzzy system. The designed fuzzy controller shares the same fuzzy sets with the fuzzy model in the premise parts. In linear matrix inequalities (LMI)-based design processes, the linear output feedback control gains are first determined so that all subsystems are stable. It is then necessary to find a common P matrix of the Lyapunov inequalities for the sufficient stability conditions. In contrast to the LMI-based method, the approach presented in this paper first assigns a desired common observability Gramian instead of the common P matrix. Subject to this specified common observability Gramian, the solutions of the linear output feedback control gains are then directly obtained by the present design methodology.
Reviewer: George S. Stavrakakis (Chania)
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93C55 | Discrete-time control/observation systems |
| 93B40 | Computational methods in systems theory (MSC2010) |
Keywords:
discrete Takagi-Sugeno fuzzy systems; observability Gramian; singular value decomposition; generalized inverse theory; parallel distributed compensationReferences:
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