Abstract
A novel approach to build a Takagi-Sugeno (T-S) fuzzy model of an unknown nonlinear system from experimental data is presented in the paper. The neuro-fuzzy models or, more specifically, fuzzy basis function networks (FBFNs) are trained from input–output data to approximate the nonlinear systems for which analytical mathematical models are not available. Then, the T-S fuzzy models are derived from the direct linearization of the neuro-fuzzy models. The operating points for linearization are chosen using the evolutionary strategy to minimize the global approximation error so that the T-S fuzzy models can closely approximate the original unknown nonlinear system with a reduced number of linearizations. Based on T-S fuzzy models, optimal controllers are designed and implemented for a nonlinear two-link flexible joint robot, which demonstrates the possibility of implementing the well-established model-based optimal control method onto unknown nonlinear dynamic systems.
Highlights
The Takagi-Sugeno (T-S) fuzzy model is a powerful and practical engineering tool for modeling and control of complex nonlinear systems
The concept of T-S fuzzy model is similar to the piecewise linear approximation approaches in nonlinear control, which linearizes a system at a set of selected operating points and designs a local linear feedback controller for each linear model
Since the overall control action is switching among the local linear controllers according to system states and there is only one local controller active at a certain time in such approaches, it can only ensure the stability and performance of the control system at the neighborhood of selected operating points [4], In contrast, the T-S fuzzy model approximates the entire nonlinear system by fuzzy inference among local linear models so that the overall control action can be generated by aggregation of local linear control laws [5]
Summary
The Takagi-Sugeno (T-S) fuzzy model is a powerful and practical engineering tool for modeling and control of complex nonlinear systems. Since the overall control action is switching among the local linear controllers according to system states and there is only one local controller active at a certain time in such approaches, it can only ensure the stability and performance of the control system at the neighborhood of selected operating points [4], In contrast, the T-S fuzzy model approximates the entire nonlinear system by fuzzy inference among local linear models so that the overall control action can be generated by aggregation of local linear control laws [5] It empowers a paradigm of designing controllers for local linear models while analyzing stability for the global nonlinear system [6]. The contribution of this paper is that it presents a practical way to build T-S fuzzy models with both good local and global approximations by deriving the direct linearization of FBFN models and introducing the evolutionary strategy for fuzzy rule location selection. This paper is organized as follows: Section 2 presents the structure of the T-S fuzzy model; Section 3 elaborates the proposed T-S fuzzy model identification approach; Section 4 explains the design of fuzzy optimal controller; Section 5 demonstrates an example of T-S model identification and optimal control of a robotic system; Section 6 concludes the paper
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