A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

Robust Multi-Criteria Optimal Fuzzy Control of Discrete-Time Nonlinear Systems

This paper presents a novel fuzzy control design of discrete-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with an inherent stability property together with a dissipativity type of disturbance reduction. The Takagi–Sugeno-type fuzzy model is used in our control system design. By solving a linear matrix inequality at each time step, the optimal control solution can be found to satisfy mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system on a cart

Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

Adaptive inferential sensors based on evolving fuzzy models

A new technique to the design and use of inferential sensors in the process industry is proposed in this paper, which is based on the recently introduced concept of evolving fuzzy models (EFMs). They address the challenge that the modern process industry faces today, namely, to develop such adaptive and self-calibrating online inferential sensors that reduce the maintenance costs while keeping the high precision and interpretability/transparency. The proposed new methodology makes possible inferential sensors to recalibrate automatically, which reduces significantly the life-cycle efforts for their maintenance. This is achieved by the adaptive and flexible open-structure EFM used. The novelty of this paper lies in the following: (1) the overall concept of inferential sensors with evolving and self-developing structure from the data streams; (2) the new methodology for online automatic selection of input variables that are most relevant for the prediction; (3) the technique to detect automatically a shift in the data pattern using the age of the clusters (and fuzzy rules); (4) the online standardization technique used by the learning procedure of the evolving model; and (5) the application of this innovative approach to several real-life industrial processes from the chemical industry (evolving inferential sensors, namely, eSensors, were used for predicting the chemical properties of different products in The Dow Chemical Company, Freeport, TX). It should be noted, however, that the methodology and conclusions of this paper are valid for the broader area of chemical and process industries in general. The results demonstrate that well-interpretable and with-simple-structure inferential sensors can automatically be designed from the data stream in real time, which predict various process variables of interest. The proposed approach can be used as a basis for the development of a new generation of adaptive and evolving inferential sensors that can a- ddress the challenges of the modern advanced process industry

New Optimal Approach for the Identification of Takagi-Sugeno Fuzzy Model

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model

An Optimal T-S Model for the Estimation and Identification of Nonlinear Functions

A novel optimal method is developed to improve the identification and estimation of Takagi-Sugeno (TS) fuzzy model. The idea comes from the fact that the main drawback of T-S model is that it can not be applied when the membership functions are overlapped by pairs. This limits the application of the T-S model because this type of membership function has been widely used in the stability and controller design of fuzzy systems. It is also very popular in industrial control applications. The method presented here can be considered as a generalized version of T-S fuzzy model with optimized performance in approximating nonlinear functions. Various examples are chosen to show the high function approximation accuracy and fast convergence obtained by applying the proposed method in approximating nonlinear systems locally and globally in comparison with the original T-S model