Huey-Jian Uang

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

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.

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

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.

Robustness design of nonlinear dynamic systems via fuzzy linear control

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.

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

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 methods tracking performance.

Fuzzy differential games for nonlinear stochastic systems: suboptimal approach

A fuzzy differential game theory is proposed to solve the n-person (or n-player) nonlinear differential noncooperative game and cooperative game (team) problems, which are not easily tackled by the conventional methods. In the paper, both noncooperative and cooperative quadratic differential games are considered. First, the nonlinear stochastic system is approximated by a fuzzy model. Based on the fuzzy model, a fuzzy controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or with the cooperative game in the sense of Pareto-optimal strategies. Using a suboptimal approach, the outcomes of the fuzzy differential games for both the noncooperative and the cooperative cases are parameterized in terms of an eigenvalue problem. Since the state variables are usually unavailable, a suboptimal fuzzy observer is also proposed in this study to estimate the states for these differential game problems. Finally, simulation examples are given to illustrate the design procedures and to indicate the performance of the proposed methods.

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

For original paper see ibid., vol. 6, p.1-11 (1998). In this correspondence, we show that the rule base implemented in the aforementioned paper cannot act as a universal approximator. Furthermore, we show by simulation that the robot example reported in the paper can be effectively controlled without need for the fuzzy component.

Fuzzy decentralized controller and observer design for nonlinear interconnected systems

In general, it is not easy to design a decentralized controller for nonlinear interconnected systems. In this study, the stability of nonlinear interconnected systems is studied via a fuzzy decentralized control method. First, the nonlinear interconnected systems are represented by an equivalent Takagi-Sugeno type fuzzy model. If the state variables are unavailable, a fuzzy observer-based state feedback controller is also proposed to solve the stability problem of nonlinear interconnected systems. A robust decentralized stabilization technique is proposed for each decentralized controller to override the effect of fuzzy approximation error and interconnection among subsystems. This design problem is equivalent to solving a linear matrix inequality problem.

Differential games for nonlinear stochastic systems: a fuzzy approach

A fuzzy differential game theory is proposed to solve the N-person (or N-player) nonlinear differential noncooperative and cooperative (team) game problems, which are not easily tackled by the conventional methods. In this study, both noncooperative and cooperative quadratic differential game are considered. First, the nonlinear stochastic system is approximated by a stochastic fuzzy model. Based on the stochastic fuzzy model, a fuzzy observer-based controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or cooperative (team) game in the sense of Pareto-optimal strategies. Using the suboptimal approach, the outcome of the fuzzy differential game for both noncooperative and cooperative game is parameterized in terms of the eigenvalue problem (EVP). Linear matrix inequality (LMI) techniques are employed to solve these problems from the convex optimization perspective.

A robustness design of uncertain nonlinear dynamic systems via fuzzy linear control

This study introduces a fuzzy linear control design method for uncertain nonlinear systems with guaranteed control performance. First, the Takagi and Sugenos fuzzy linear model is employed to approximate an uncertain nonlinear systems. Next, based on fuzzy linear model, a fuzzy controller is developed to stabilize the fuzzy linear model and at the same time the effect of fuzzy approximation error on control performance is attenuated to a prescribed level. Finally, a robustness performance is achieved in the uncertain nonlinear control system. In the proposed fuzzy linear control method, the fuzzy linear model plays the role of rough control to approximate the nonlinear control system and the H/sup /spl infin// scheme plays the role of precise control to achieve a robustness performance. Linear matrix inequality (LMI) techniques will be employed to treat this robustness fuzzy control problem. If the state variables are unavailable, a fuzzy observer-based H/sup /spl infin// control is also proposed to achieve the robustness design of nonlinear uncertain systems.