Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed

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A Survey on Analysis and Design of Model-Based Fuzzy Control Systems

New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI

This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H/sub /spl infin// model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method.

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Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model

This study introduces a mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H/sub 2//H/sub /spl infin// controller is developed to achieve the suboptimal H/sub 2/ control performance with a desired H/sub /spl infin// disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H/sub 2//H/sub /spl infin// control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method.

Mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach

This study introduces a fuzzy linear control design method for nonlinear systems with optimal H/sup /spl infin// robustness performance. First, the Takagi and Sugeno fuzzy linear model (1985) is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. Thus based on the fuzzy linear model, H/sup /spl infin// performance design can be achieved in nonlinear control systems. In the proposed fuzzy linear control method, the fuzzy linear model provides rough control to approximate the nonlinear control system, while the H/sup /spl infin// scheme provides precise control to achieve the optimal robustness performance. Linear matrix inequality (LMI) techniques are employed to solve this robust fuzzy control problem. In the case that state variables are unavailable, a fuzzy observer-based H/sup /spl infin// control is also proposed to achieve a robust optimization design for nonlinear systems. A simulation example is given to illustrate the performance of the proposed design method.

Robustness design of nonlinear dynamic systems via fuzzy linear control

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance.

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Robust tracking enhancement of robot systems including motor dynamics: a fuzzy-based dynamic game approach

characterized in terms of cross-coupled Hamilton‐Jacobi‐Issacs partial differential equations. Until now, it is still very difficult to solve cross-coupled Hamilton‐Jacobi‐Issacs partial differential equations either analytically or numerically. Since the optimal solution for the mixed control problem of nonlinear systems is hardly obtained, it turns out to be interesting in seeking the suboptimal solution for the mixed control problem of nonlinear systems. Furthermore, state variables are often unavailable in nonlinear systems. In this situation, mixed output feedback control is more appealing for practical application. In this study, based on a suboptimal approach, a fuzzy observer-based mixed control design is proposed to achieve the suboptimal control performance under a desired disturbance rejection constraint.

Huey-Jian Uang

Papers

Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model

Mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach

Robustness design of nonlinear dynamic systems via fuzzy linear control

Robust tracking enhancement of robot systems including motor dynamics: a fuzzy-based dynamic game approach

Mixed Fuzzy Output Feedback Control Design for Nonlinear Dynamic Systems: An LMI Approach