Jesús A. Meda-Campaña

Exact Output Regulation for Nonlinear Systems Described by Takagi–Sugeno Fuzzy Models

The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T-S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.

The fuzzy discrete-time robust regulation problem: an LMI approach

This paper is concerned with the design of a robust regulator capable of achieving trajectory tracking for discrete-time nonlinear systems under parameter uncertainty. By assuming that the behavior of the nonlinear system is described, at least locally, by a Takagi-Sugeno dynamic fuzzy model, an approach based in the combination of this fuzzy modeling and the regulator theory is presented. Conditions for the existence of a robust regulator under this approach are then derived and extended to include the use of the linear matrix inequality (LMI) technique.

Analysis of the Fuzzy Controllability Property and Stabilization for a Class of T–S Fuzzy Models

In this paper, the controllability property for a class of Takagi-Sugeno (T-S) fuzzy models is analyzed, while a fully nonlinear stabilizer is designed in a practical way. It is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach. The existence of such controllers depends on the fuzzy controllability conditions, which are derived in a straightforward way. The main advantage of the proposed approach is that the convergence of the closed-loop system can be imposed arbitrarily. Some examples are given in order to illustrate the validity of the method. Finally, the proposed controller is applied on an underactuated system known as “pendubot” and the results are compared with an stabilizer designed on the basis of LMIs.

The fuzzy discrete-time robust regulation problem: a LMI approach

This work is concerned with the design of a robust regulator, capable of achieving trajectory tracking for discrete-time nonlinear systems under parameter uncertainty. It is assumed that the behavior of the nonlinear system is described, at least locally, by a Takagi-Sugeno dynamic fuzzy model, an approach based in the combination of this fuzzy modelling and the regulator theory is presented. Condition for the existence of a robust regulator under this approach are then derived and extended to include the use of the LMI technique.

Discrete-time Kalman filter for Takagi–Sugeno fuzzy models

In this work, the Kalman Filter (KF) and Takagi–Sugeno fuzzy modeling technique are combined to extend the classical Kalman linear state estimation to the nonlinear field. The framework for such extension is given, and in this sense the discrete-time fuzzy Kalman filter (DFKF) is obtained. It will be shown that the fuzzy version gives some advantages when is compared with the Extended Kalman Filter (EKF), which is the most typical extension of the KF to the nonlinear field. The proposed approach provides a significantly smaller processing time than the processing time of the EKF while the mean square error is also reduced. Finally, some examples, such as the Lorenz chaotic attractor and under actuated mechatronic system (pendubot), are used to compare the DFKF and EKF.

On the Nonlinear Fuzzy Regulation for under-actuated systems

In this paper, the Takagi-Sugeno (TS) fuzzy modelling and the nonlinear regulation theory are combined in order to construct a controller capable of taking the output of the fuzzy plant to the reference signal generated by an external system. The fuzzy modelling allows the controller to be designed by means of numerical techniques while the resulting stability region is larger than those obtained when simple linear controllers are used to stabilize nonlinear systems. On the other hand, it is well-known that a fuzzy regulator constructed from linear controllers does not solve the regulation problem in general. Therefore, a fully nonlinear regulator is considered in this work. The results are applied on the pendubot, which is an under-actuated electromechanical system with very complex nonlinear dynamics.

Stability Analysis for Autonomous Dynamical Switched Systems through Nonconventional Lyapunov Functions

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

Tuning of a TS Fuzzy Output Regulator Using the Steepest Descent Approach and ANFIS

The exact output regulation problem for Takagi-Sugeno (TS) fuzzy models, designed from linear local subsystems, may have a solution if input matrices are the same for every local linear subsystem. Unfortunately, such a condition is difficult to accomplish in general. Therefore, in this work, an adaptive network-based fuzzy inference system (ANFIS) is integrated into the fuzzy controller in order to obtain the optimal fuzzy membership functions yielding adequate combination of the local regulators such that the output regulation error in steady-state is reduced, avoiding in this way the aforementioned condition. In comparison with the steepest descent method employed for tuning fuzzy controllers, ANFIS approximates the mappings between local regulators with membership functions which are not necessary known functions as Gaussian bell (gbell), sigmoidal, and triangular membership functions. Due to the structure of the fuzzy controller, Levenberg-Marquardt method is employed during the training of ANFIS.

On the exact output regulation for Takagi-Sugeno fuzzy systems

In this paper, the Takagi-Sugeno (TS) fuzzy modelling and the fuzzy regulation theory are considered in order to design a fuzzy controller capable of taking the output of a fuzzy plant to the reference signal generated by an external system. It is well-known that TS fuzzy modelling allows the stabilizer to be obtained by means of numerical techniques. As a result, stability region defined by the fuzzy stabilizer is larger than the one obtained when a simple linear stabilizer is considered. On the other hand, a fuzzy regulator constructed from linear controllers does not solve the exact regulation problem in general [6], [12], [13], [15]. Therefore, a fully nonlinear regulator, defined on the overall TS fuzzy model, is considered in this work. The results are applied on a simple fuzzy model in order to illustrate the improvement achieved with the proposed approach.

Hybrid Architecture for Coordination of AGVs in FMS

This paper presents a hybrid control architecture that coordinates the motion of groups of automated guided vehicles in flexible manufacturing systems. The high-level control is based on a Petri net model, using the industrial standard ISA-95, obtaining a task-based coordination of equipment and storage considering process restrictions, logical precedences, shared resources and the assignment of robots to move workpieces individually or in subgroups. On the other hand, in the low-level control, three basic control laws are designed for unicycle-type robots in order to achieve desired formation patterns and marching behaviours, avoiding inter-robot collisions. The control scheme combines the task assignment for the robots obtained from the discrete-event model and the implementation of formation and marching continuous control laws applied to the motion of the mobile robots. The hybrid architecture is implemented and validated for the case of a flexible manufacturing system and four mobile robots using a virtual reality platform.