T. Taniguchi

Fuzzy descriptor systems: stability analysis and design via LMIs

A fuzzy descriptor system is defined. Six kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities (LMIs). The stability analysis is reduced to a problem of finding a common Lyapunov function. An LMI design approach is employed to find stable feedback gains and a common Lyapunov function.

Model-based fuzzy control of TORA system: fuzzy regulator and fuzzy observer design via LMIs that represent decay rate, disturbance rejection, robustness, optimality

This paper presents a model-based fuzzy control of translational oscillations with a proof mass actuator (TORA) which is well known as a nonlinear control benchmark problem. The fuzzy regulator and fuzzy observer are designed by solving linear matrix inequalities (LMIs) that represent control performance such as the decay rate, disturbance rejection, robust stability, minimization of quadratic performance function and constraints on the control input and output. Simulation results show the utility of the model-based fuzzy control utilizing the LMIs.

Fuzzy control based on quadratic performance function-a linear matrix inequality approach

Presents an LMI approach to optimal fuzzy control based on a quadratic performance function. First, stability conditions are presented by relaxing the previous stability results. The relaxed stability conditions are represented in terms of LMIs. The optimal fuzzy controller design utilizing the relaxed stability conditions is proposed. The optimal fuzzy controller is designed by solving the minimization problem that minimizes the upper bound of a given quadratic performance function. Finally, a design example for the well-known nonlinear control benchmark problem, the TORA system, demonstrates the utility of the optimal fuzzy control based on a quadratic performance function.

Robust and optimal fuzzy control: A linear matrix inequality approach

Abstract This paper presents a mixed control design of robust fuzzy control and optimal fuzzy control based on relaxed stability conditions represented by linear matrix inequalities (LMIs). A robust fuzzy controller is designed so as to maximize the norm of the uncertain blocks in a Takagi-Sugeno fuzzy model. Next, an optimal fuzzy controller is designed by solving the minimization problem that minimizes the upper bound of a given quadratic performance index. A mixed control problem that simultaneously considers both of them is defined and is efficiently solved via convex optimization techniques based on LMIs. Finally, a design example for a nonlinear control benchmark problem demonstrates the utility of the mixed control problem based on LMIs.

Nonlinear model following control via Takagi-Sugeno fuzzy model

Presents a unified approach to nonlinear model following control that contains the regulation and servo control problems as special cases. A parallel distributed compensation (PDC) for fuzzy reference models is proposed. The PDC fuzzy controller mirrors the structures of Takagi-Sugeno fuzzy models that represent a nonlinear system and a nonlinear reference model. We present a linearization technique as a basic result. Conditions to linearize the error system between the feedback system and the nonlinear reference model are obtained in terms of linear matrix inequalities (LMIs). Design examples are illustrated to show the utility of the nonlinear model following control.

Generalized Takagi-Sugeno fuzzy systems: rule reduction and robust control

Presents model reduction and robust control using a generalized form of Takagi-Sugeno fuzzy systems. We first define a generalized form of Takagi-Sugeno fuzzy systems. The generalized form has a decomposed structure for each element of A/sub i/ and B/sub i/ matrices in consequent parts. The key feature of this structure is that it is suitable for reducing the number of rules. Conditions to reduce the number of rules are represented in terms of LMIs. The main idea is to find a structure of if-then rules of the reduced model that agrees well with dynamics of the original model. Furthermore, we estimate the lower bound of the norm of model uncertainty of the Takagi-Sugeno fuzzy system that can cover the reduction error. Finally, an example of model reduction and robust control for a nonlinear system is illustrated. In this example, we achieve a robust controller design so as to compensate the uncertainly of the Takagi Sugeno fuzzy system.

A new PDC for fuzzy reference models

This paper presents a relaxed approach that provides relaxed LMI conditions for effectively achieving the nonlinear model following control. The proposed method is a unified approach to nonlinear model following control that contains the regulation and servo control problems as special cases. Furthermore, we present a new parallel distributed compensation (PDC). Design examples are illustrated to show the utility of the relaxed approach for nonlinear model following control.

Trajectory control of an articulated vehicle with triple trailers

Presents backing up control for a vehicle with triple trailers. In particular, we consider constraints on input and output and disturbance rejection that are incorporated in the LMI conditions. In application to the truck with triple trailers setup, we utilize these LMI conditions to explicitly avoid the saturation of the steering angle and the jack-knife phenomenon in the control design. The simulation and experimental results demonstrate that the controller effectively achieves the backing up control of the vehicle with triple trailers while avoiding the saturation of the actuator and jack-knife phenomenon. Moreover, the feedback controller guarantees the stability and performance even for disturbance.

Model-based fuzzy control for two trailers problem: stability analysis and design via linear matrix inequalities

We design a backward movement control system for a vehicle with two trailers via a model-based fuzzy control technique. A Takagi-Sugeno fuzzy model is constructed to describe the nonlinear dynamics of the vehicle. The so-called parallel distributed compensation is employed to determine a control rule structure of a fuzzy controller from the fuzzy model of the vehicle. The parameters of the fuzzy controller are obtained via the linear matrix inequality (LMI) based design with respect to the decay rate, constraint on the control input and constraint on the output. Simulation and experimental results show that the fuzzy controller designed effectively achieves the backward movement control of the articulated vehicle without using the jack-knife phenomenon.

Fuzzy control of a vehicle with two trailers

We design a backward movement control system for a vehicle with two trailers. A linear matrix inequality (LMI) based design that considers stability, decay rate and constraints on control input and output is employed to design a fuzzy controller. Simulation and experimental results show that the designed fuzzy controller effectively achieves the backward movement control.