Simultaneous Linear Control for Non-linear Uncertain Systems Described by Takagi-Sugeno Fuzzy Model

Nonlinearities and system uncertainties are the most important difficulties in designing controllers that ensure stability and acceptable closed-loop performance. Many significant results on the stability and robust control of uncertain nonlinear systems using the TS fuzzy model have been reported over the past decades, and considerable advances have been made (Connor et al. 1992; Chen et al. 1996; Rocha et al. 2005; Boukhezzar et al. 2006; Kamal et al. 2011, 2012a, 2013; Khanl et al. 2011). However, as stated in Khan and Hossain (2011), many approaches for stability and robust control of uncertain systems are often characterized by conservatism when dealing with uncertainties. It has been well known that the TS fuzzy model is very effective representation of complex nonlinear systems. In the TS fuzzy model, the state space of a nonlinear system is divided into different fuzzy regions with a local linear model being used in each region. The overall model output is obtained by defuzzification using the center of gravity (COG) method. Once the fuzzy model is obtained, control design can be carried out via the so-called parallel and distributed computing (PDC) approach, which employs multiple linear controllers corresponding to the locally linear plant models (Boukhezzar et al. 2006). This class of systems is described as a weighted sum of some simple linear subsystems, and thus is easily analyzable.

This paper addresses the issue of tracking the output of an activated sludge process using fuzzy integral control. First, the dynamics of the nonlinear process are modeled with a dynamic state space fuzzy model integrating the effect of external disturbances, and then an additional integral state of the output tracking error is introduced to obtain an augmented Takagi-Sugeno (TS) fuzzy model. The TS fuzzy model is able to describe the dynamics of complex nonlinear systems with an excellent degree of accuracy. It is formulated by fuzzy if-then rules which can give local linear representation of the overall nonlinear system. Second, the design of the fuzzy integral control is performed, in which the state feedback gains are obtained by solving linear matrix inequalities (LMI). The objective is to ensure trajectory tracking of an activated sludge process (ASP) by controlling two key variables: the substrate concentration and the level of dissolved oxygen. To assess the performance of the proposed control strategy, a comparative analysis is carried out with a gain scheduling PI (GS-PI) controller. Simulation results are provided to illustrate the effectiveness of the proposed approach. Where, the fuzzy integral control reduces the high energy consumption in water treatment plants.

In this paper, a model predictive control (MPC) scheme is investigated for uncertain nonlinear system with time delay and input constraint. First, the Takagi-Sugeno (T-S) fuzzy model is used to approximate the dynamics of nonlinear processes and the parallel distributed compensation (PDC) controllers which are parameter dependent and mirror the structure of the T-S plant model are proposed. Then a novel feedback PDC predictive controller obtained from the linear matrix inequality (LMI) solutions which can guarantee the stability of the closed-loop overall fuzzy system is put forward. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed method.

This paper introduces a novel adaptive inverse multilayer T-S fuzzy controller (AIMFC) optimally identified with an optimization soft computing algorithm available for a class of robust control applied in uncertain nonlinear SISO systems. The parameters of multilayer T-S fuzzy model are optimally identified by the differential evolution (DE) algorithm to create offline the inverse nonlinear plant with uncertain coefficients. Then, the adaptive fuzzy-based sliding mode surface is applied to ensure that the closed-loop system is asymptotically stable in which the stability is satisfied using Lyapunov stability concept. The control quality of the proposed AIMFC algorithm is compared with the three recent advanced control algorithms applied in the Spring-Mass-Damper (SMD) benchmark system. Simulation and experiment results with different control parameters show that the proposed algorithm is better than the inverse fuzzy controller and the conventional adaptive fuzzy controller comparatively applied in both SMD system and the coupled-liquid tank system with the performance index using the least mean squares (LMS) error, which is investigated to demonstrate the efficiency and the robustness of the proposed AIMFC control approach.

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

This paper deals with the problem of robust control for Uncertain Nonlinear System via fuzzy control approach. First, a fuzzy controller with robust control capability is proposed. For avoiding complex controller parameters adjustment, Multi-objective particle swarm Optimization (PSO) algorithm is adopted during the controller design. Secondly, the multi-model is employed to represent the nonlinear system with norm-bounded parameter uncertainties. Finally, a simulation example illustrates the effectiveness and the feasibility of the proposed approach.

The primary aim of a vehicle's suspension system is to isolate the vehicle's main body from road irregularities, thus improving passenger comfort and ensuring optimal handling stability. This research discusses a stabilizing fuzzy control design for active vehicle suspension systems. The nonlinear model of the active suspension is then represented using a Takagi-Sugeno (TS) fuzzy model. The control approach uses a TS fuzzy controller utilizing an observer to estimate the state while reducing road disturbances. The closed-loop stability requirements of the vehicle utilizing the fuzzy controller and observer are expressed as a Linear Matrix Inequalities (LMI) problem, which can be effectively resolved through convex optimization methods. In this paper, we study the stability of the nonlinear automotive active suspension system with two degrees of freedom represented by a TS fuzzy model, where we will present the stabilization conditions by state feedback via the PDC (Parallel Distributed Compensation) control law and in the last section we introduced the TS fuzzy observer for the case of non-measurable premise variables.

This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.

Over the past two decades, there has been a rapidly growing interest in approximating a nonlinear system by a Takagi-Sugeno (T-S) fuzzy model (Takagi & Sugeno, 1985). In general, this model is represented by using a set of fuzzy rules to describe a global nonlinear system in terms of a set of local linear models which are smoothly connected by fuzzy membership functions. Based on the T-S fuzzy model, recently, various fuzzy controllers have been developed under the so-called parallel-distributed compensation (PDC) scheme (in which each control rule is distributively designed for the corresponding rule of a T-S fuzzy model) and have been widely and successfully applied in fields ranging from aerospace to process control. The reason is because the fuzzy model-based control method provides a natural, simple and effective design approach to complement other nonlinear control techniques that require special and rather involved knowledge. Below are listed the main features of T-S model-based fuzzy control method: 1. It does not require severe structural assumptions on the plant model. 2. It preserves well-understood linear intuition. 3. It is naturally compatible with decompositions of the overall control problem. The decompositions are typically not hierarchical, and the interactions of sub-problems are captured by physical variables that are typically state variables in a more complete model of the overall system. 4. It enables control systems to respond rapidly to changing operating conditions. For this reason, it is important that the selected physical variables reflect changes in plant dynamics as operating conditions change. In fact, the T-S model-based fuzzy control method (of divide and conquer type) constructs a nonlinear controller, with certain required dynamic properties, by combining, in some sense, the members of appropriate family of linear time-invariant controllers. Here, nonlinear control design task is broken into a number of linear sub-problems, which enable linear design methods to be applied to nonlinear problems. Within the general framework of the T-S fuzzy model-based control method, a flurry of research activities have quickly yielded many important results on the design of fuzzy control systems by means of the following Lyapunov function approaches: 1. Common quadratic Lyapunov function approach (Tanaka & Sugeno, 1992; Tanaka et al, 1996; Wang et al, 1996; Cao & Frank, 2000; Assawinchaichote, 2004).

This paper addresses the analysis and design of fuzzy control systems for a class of complex uncertain single input single output nonlinear systems. In the design procedure, we represent the nonlinear system using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller by blending all local state feedback controllers with a sliding mode controller. Unlike the commonly used parallel distributed compensation technique, we can design a global stable fuzzy controller without finding a common Lyapunov function for all local control systems, and can obtain a good tracking performance. Furthermore, a stability analysis is carried out not for the fuzzy model but for a real nonlinear system with uncertainties. One simulation example is given to show the effectiveness and feasibility of the proposed fuzzy controller design method.

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of nonlinear interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected systems. Finally, an example is given to illustrate the concepts discussed throughout the paper.

This paper presents novel Takagi-Sugeno (T-S) fuzzy model-based robust finite time control methods for a class of uncertain nonlinear systems. First, the nonlinear system is approximated by a suitable T-S fuzzy model in which most of the parameters can be computed offline. Then, a T-S fuzzy model-based nonsingular terminal sliding mode control (TS-NTSMC) method is designed based on a proposed nonsingular terminal sliding mode (NTSM) surface. This method not only alleviates the online computational burden, but also preserves the advantages of fast and finite time convergence, high tracking precision, and robustness to uncertainties and disturbances. However, the discontinuous function [Formula: see text] causes the chattering phenomenon, which is unavoidable. In order to attenuate the chattering, maintain the key properties of the TS-NTSMC method and achieve higher control performance, a novel T-S fuzzy model-based super-twisting higher order nonsingular terminal sliding mode control (TS-STHONTSMC) method is proposed. The global finite time stability of the resulting closed-loop systems is analytically proven herein. Two numerical simulations are presented to illustrate the effectiveness and applicability of the proposed control methods and to validate the theoretical results.

In this paper, the issue of human behavior learning (HBL) is addressed for a class of nonlinear human-in-the-loop (HiTL) systems where the human operator is viewed as a nonlinear optimal controller. Owing to its outstanding interpretability and strong nonlinear representation capability, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear HiTL control system and approximate the unknown human control law based on the parallel distributed compensation (PDC) scheme. A quadratic-like cost function with fuzzy weighting matrices is built to depict the human behavior, which conforms to human thinking and is unknown to the machine. The aim of the HBL is to retrieve the fuzzy weighting matrices such that the human control law will be optimal in the sense of minimizing the retrieved cost function. In the proposed HBL scheme, the state-dependent Riccati equation (SDRE) based nonlinear optimal control technique plays an important role, which has a similar structure to the linear quadratic regulator (LQR) theory and thus is of low computational complexity. With the help of the PDC based fuzzy approximator for the unknown human control law, a two-step procedure is proposed for the HBL. First, a filter-based adaptive law is developed to learn the gain matrices of the fuzzy approximator using the system state data only. The convergence analysis of the adaptive estimator is also given. Then, a semidefinite programming (SDP) problem with the quadratic objective function can be set up for determining the fuzzy weighting matrices of the cost function. The simulation study on a steering control system of the intelligent vehicle is given to show the effectiveness and applicability of the developed approach.

This paper proposes a novel adaptive synchronization approach for a class of nonlinear large-scale systems via T-S fuzzy model. It is known that the practical large-scale systems are very complicated with nonlinear coupling strength between every two subsystems, thus the classical linear control methods are invalid for them. To overcome this deficiency, we employ the T-S fuzzy model in this paper. Firstly, the local linearization approach is utilized to preprocess the nonlinear large-scale systems, and then, according to the universal approximation property of TS fuzzy model, a new system model is established. Secondly, the fuzzy adaptive synchronization controllers are designed by using Parallel Distributed Compensation technique and the corresponding stability analysis is presented through Lyapunov technique. In addition, a new criterion, under which the proposed control scheme can be transformed into pinning control and save unnecessary costs, is also given. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.