Adaptive fuzzy sliding mode controller for a class of SISO nonlinear time-delay systems

In this paper, we propose an adaptive fuzzy controller for a class of nonlinear SISO time-delay systems. The plant model structure is represented by a Takagi–Sugeno (T–S) type fuzzy system. The T–S fuzzy model parameters are adjusted online. The proposed algorithm utilizes the sliding surface to adjust online the parameters of T–S fuzzy model. The controller is based on adjustable T–S fuzzy parameters model and sliding mode theory. The stability analysis of the closed-loop system is based on the Lyapunov approach. The plant state follows asymptotically any bounded reference signal. Two examples have been used to check performances of the proposed fuzzy adaptive control scheme.     

Robust output tracking control for discrete-time nonlinear systems with time-varying delay: Virtual fuzzy model LMI-based approach

This paper proposes an output tracking control via virtual reference model for a class of nonlinear discrete-time systems with time-varying delay and disturbance. First, a Takagi–Sugeno (T–S) fuzzy model represents the discrete-time nonlinear system with time-varying delay. Second, a fuzzy observer design estimates immeasurable state. Third, a virtual desired variable (VDV) based tracking controller design guarantees H_∞ control performance for the overall system. Using Lyapunov’s stability analysis, we obtain sufficient conditions for stability of estimation, control, and robustness. The advantages are as follows: (i) allow unknown time-varying delay; (ii) ensure robust output tracking; (iii) provide relaxed conditions via a three-steps procedure to find observer and controller gain. To verify the theoretical derivation, we carry out numerical simulations on a stirred tank reactor system as an example. Satisfactory results validate the claims.     

Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.     

基于模糊观测器T-S模型和自适应模糊逻辑系统的一类非线性系统的H∞控制

针对一类非线性系统，把模糊T-S模型和自适应模糊逻辑系统两类模糊逻辑方式结合起来，提出了一种基于观测器的控制方案．首先，应用模糊T-S模型对非线性系统建模，设计观测器来观测系统状态；由线性矩阵不等式得到模糊模型的控制律．其次，应用自适应模糊逻辑系统作为补偿器来补偿建模误差．证明了闭环系统满足期望的性能．仿真结果表明了该方案的可行性．     

Output feedback controller design of Takagi–Sugeno fuzzy systems

This paper presents new systematic design methods of two types of output feedback controllers for Takagi–Sugeno (T–S) fuzzy systems, one of which is constructed with a fuzzy regulator and a fuzzy observer, while the other is an output direct feedback controller. In order to use the structural information in the rule base to decrease the conservatism of the stability analysis, the standard fuzzy partition (SFP) is employed to the premise variables of fuzzy systems. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The concept of parallel distributed compensation (PDC) is employed to design fuzzy regulators and fuzzy observers from the T–S fuzzy models. New stability analysis and design methods of output direct feedback controllers are also presented. The output feedback controllers design and simulation results for a nonlinear mass-spring-damper mechanical system show that these methods are effective.     

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACT

This study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.     

Adaptive fuzzy identification and predictive control for industrial processes

This paper proposes a method for adaptive identification and control for industrial applications. The learning of a T–S fuzzy model is performed from input/output data to approximate unknown nonlinear processes by a hierarchical genetic algorithm (HGA). The HGA approach is composed by five hierarchical levels where the following parameters of the T–S fuzzy system are learned: input variables and their respective time delays, antecedent fuzzy sets, consequent parameters, and fuzzy rules. In order to reduce the computational cost and increase the algorithm’s performance an initialization method is applied on HGA. To deal with nonlinear plants and time-varying processes, the T–S fuzzy model is adapted online to maintain the quality of the identification/control. The identification methodology is proposed for two application problems: (1) the design of data-driven soft sensors, and (2) the learning of a model for the Generalized predictive control (GPC) algorithm. The integration of the proposed adaptive identification method with the GPC results in an effective adaptive predictive fuzzy control methodology. To validate and demonstrate the performance and effectiveness of the proposed methodologies, they are applied on identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment system; and on control of a simulated continuous stirred tank reactor (CSTR) and on a real experimental setup composed of two coupled DC motors. The results are presented, showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily and it can be used successfully as a prediction model of the process for the GPC controller.     

Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common P matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.     

An Indirect Adaptive Fuzzy Control Scheme for a Class of Nonlinear Systems

This paper presents an indirect adaptive control scheme, for a class of nonlinear systems in controller canonical form. Owing to the universal approximation property of a Takagi–Sugeno (T–S) fuzzy model, controller design is simplified by utilizing the T–S fuzzy model representation of a nonlinear system. An adaptation mechanism ensures that the estimator model asymptotically follow the actual T–S fuzzy model and thus removes the need of any a priori identification of the T–S fuzzy model of the system. The overall controller gain is a convex combination of the local linear gains which vary adaptively to ensure the convergence of the tracking error. Preliminary simulation results indicate the potential of the proposed method.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust fuzzy control of nonlinear stochastic delay systems with impulsive effects

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive stochastic systems with time-varying delays is investigated. The nonlinear delay system is represented by the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for mean square exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the applicability of the theoretical results.     

Multiple fuzzy model-based temperature predictive control for HVAC systems

In this paper, a multiple model predictive control (MMPC) strategy based on Takagi–Sugeno (T–S) fuzzy models for temperature control of air-handling unit (AHU) in heating, ventilating, and air-conditioning (HVAC) systems is presented. The overall control system is constructed by a hierarchical two-level structure. The higher level is a fuzzy partition based on AHU operating range to schedule the fuzzy weights of local models in lower level, while the lower level is composed of a set of T–S models based on the relation of manipulated inputs and system outputs correspond to the higher level. Following this divide-and-conquer strategy, the complex nonlinear AHU system is divided into a set of T–S models through a fuzzy satisfactory clustering (FSC) methodology and the global system is a fuzzy integrated linear varying parameter (LPV) model. A hierarchical MMPC strategy is developed using parallel distribution compensation (PDC) method, in which different predictive controllers are designed for different T–S fuzzy rules and the global controller output is integrated by the local controller outputs through their fuzzy weights. Simulation and real process testing results show that the proposed MMPC approach is effective in HVAC system control applications.     

Modeling of an inverted pendulum based on fuzzy clustering techniques

The inverted pendulum is a highly nonlinear and open loop unstable system. To develop an accurate model of the inverted pendulum, different linear and nonlinear methods of identification will be used. However one of the problems encountered during modeling is the collection of experimental data from the inverted pendulum system. Since the output data from the unstable system does not show enough information or dynamics of the system. This can be overcome by designing a feedback controller, which stabilize the system before identification can takes place. Recently Takagi–Sugeno (T–S) fuzzy modeling based on clustering techniques have shown great progress in identification of nonlinear systems. Hence in this paper, Takagi–Sugeno (T–S) model is proposed for an inverted pendulum based on fuzzy c-means, Gustafson–Kessel (G–K) and Gath–Geva clustering techniques. Simulation results show that Gustafson–Kessel (G–K) clustering technique produces satisfactory performance.     

Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach

This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.     

Analysis and synthesis of discrete nonlinear passive systems via affine T–S fuzzy models

The article considers the analysis and synthesis problem for the discrete nonlinear systems, which are represented by the discrete affine Takagi–Sugeno (T–S) fuzzy models. The state feedback fuzzy controller design methodology is developed to guarantee that the affine T–S fuzzy models achieve Lyapunov stability and strict input passivity. In order to find a suitable fuzzy controller, an Iterative Linear Matrix Inequality (ILMI) algorithm is employed in this article to solve the stability conditions for the closed-loop affine T–S fuzzy models. Finally, the application of the proposed fuzzy controller design methodology is manifested via a numerical example with computer simulations.     

A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems

This paper presents a sum of squares (SOS) approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi--Sugeno (T--S) fuzzy modeling and control. First, we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well-known T--S fuzzy modeling and control. Secondly, we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing LMI-based approaches to T--S fuzzy modeling and control. Moreover, the derived stability and stabilizability conditions are represented in terms of SOS and can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. To illustrate the validity and applicability of the proposed approach, a number of analysis and design examples are provided. The first example shows that the SOS approach renders more relaxed stability results than those of both the LMI-based approaches and a polynomial system approach. The second example presents an extensive application of the SOS approach in comparison with a piecewise Lyapunov function approach. The last example is a design exercise that demonstrates the viability of the SOS-based approach to synthesizing a stabilizing controller.      

An improved sum‐of‐squares based approach to fuzzy tracking control design of nonlinear systems

In this paper, using a more general Lyapunov function, less conservative sum‐of‐squares (SOS) stability conditions for polynomial‐fuzzy‐model‐based tracking control systems are derived. In tracking control problems the objective is to drive the system states of a nonlinear plant to follow the system states of a given reference model. A state feedback polynomial fuzzy controller is employed to achieve this goal. The tracking control design is formulated as an SOS optimization problem. Here, unlike previous SOS‐based tracking control approaches, a full‐state‐dependent Lyapunov matrix is used, which reduces the conservatism of the stability criteria. Furthermore, the SOS conditions are derived to guarantee the system stability subject to a given H_∞ performance. The proposed method is applied to the pitch‐axis autopilot design problem of a high‐agile tail‐controlled pursuit and another numerical example to demonstrate the effectiveness and benefits of the proposed method.     

Non-monotonic robust H2 fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H₂ fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T–S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H₂ fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.     

Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method

In this study, we present a Takagi–Sugeno (T–S) fuzzy model for the modeling and stability analysis of oceanic structures. We design a nonlinear fuzzy controller based on a parallel distributed compensation (PDC) scheme and reformulate the controller design problem as a linear matrix inequalities (LMI) problem as derived from the fuzzy Lyapunov theory. The robustness design technique is adopted so as to overcome the modeling errors for nonlinear time-delay systems subject to external oceanic waves. The vibration of the oceanic structure, i.e., the mechanical motion caused by the force of the waves, is discussed analytically based on fuzzy logic theory and a mathematical framework. The end result is decay in the amplitude of the surge motion affecting the time-delay tension leg platform (TLP) system. The feedback gain of the fuzzy controller needed to stabilize the TLP system can be found using the Matlab LMI toolbox. This proposed method of fuzzy control is applicable to practical TLP systems. The simulation results show that not only can the proposed method stabilize the systems but that the controller design is also simplified. The effects of the amplitude damping of the surge motion on the structural response are obvious and work as expected due to the control force.