A Non-Fragile H∞ Output Feedback Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales

This paper presents a Takagi-Sugeno (TS) fuzzy state-feedback controller based on a linear matrix inequality (LMI) approach for the permanent magnet synchronous generator of wind energy conversion system (PMSG-WECS). A dc/dc converter is considered to regulate the maximum power output of the system. To show its effectiveness, the dynamic model is replaced by the TS fuzzy model, which the proposed controller can be applied to the PMSG-WECS, while the controller gains can be obtained by solving set of a LMI approach. The proposed controller guarantees the stability of the system. Therefore, the performance of the proposed TS fuzzy state-feedback controller is assessed through the computer simulation.

This paper deals with the problem of robust Sliding Mode Control (SMC) of uncertain nonlinear dynamic systems. The uncertainties being norm bounded in both state and input matrices as well as norm bounded nonlinearity. Sufficient conditions using Linear Matrix Inequalities (LMIs) are derived to guarantee the existence of linear sliding surface and the quadratic stability of the reduced-order equivalent dynamic system restricted to the sliding surface. Thus, one can design a continuous nonlinear control strategy ensuring a sliding motion despite the presence of uncertainties. We analysis and applies the designed controller to a flexible joint robotic system, in which the simulations results are validate its effectiveness and good performance.

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.

This paper studies the fuzzy H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filter design problem for signal estimation of nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. First, the Takagi-Sugeno (T-S) fuzzy model is used to represent the state-space model of nonlinear discrete-time systems with time delays. Next, we design a stable fuzzy H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filter based on the T-S fuzzy model, which guarantees asymptotic stability and a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> index for the filtering error system, irrespective of the time delays and uncertain disturbances. A sufficient condition for the existence of such a filter is established by using the linear matrix inequality (LMI) approach. The proposed LMI problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the present method.

The problem of fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control is investigated for a class of nonlinear systems with time-varying delay. Specifically, the considered system is approximated by a Takagi-Sugeno (T-S) fuzzy model. By using linear matrix inequality (LMI) methods, we design a fuzzy static output feedback H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controller, which guarantees asymptotic stability and a prescribed H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> index for the resulting closed-loop system. In contrast to the existing results, the gains of controller are obtained by solving a set of LMIs. The proposed method is easy to implement and can be applied to linear systems. A numerical example is provided to illustrate the effectiveness of the developed method.

In this paper, a stable fuzzy controller in the form of linear matrix inequalities (LMIs) is designed for an electric vehicle (EV). The proposed controller evaluates the stabilization of the EV speed with robust disturbance rejection approach throughout both transient and steady states and in the presence of external disturbances and parametric uncertainties. In order to achieve an efficient control, EV's battery voltage, as control input, and EV speed, as system output, are constrained. The proposed control strategy is based on Takagi-Sugeno (T-S) fuzzy model and the parallel distributed compensation (PDC) fuzzy controller. Proposed controller can be practically implemented due to low computational load of control input that is owing to the offline process of obtaining the feedback gains, very small amplitude of control input and low power consumption. To evaluate the performance of the designed controller, simulations in five steps are conducted on an EV equipped with a brushed direct current (BDC) motor as a case study in MATLAB simulation environment. Ultimately, the real-time digital simulation results using real-time digital power system simulator (RTDS) confirm the efficiency of the proposed input-output constrained robust disturbance rejection stable fuzzy controller (IOCRDRSFC) in stabilizing the EV speed. The simulation results obtained from MATLAB and the RTDS confirm the energy-efficient and robust performance of the proposed controller in quick stabilization of the EV speed in the presence of all structured and unstructured uncertainties.

This paper addresses stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. First, the Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties is used as the model for the uncertain nonlinear system. Based on the fuzzy Lyapunov function approach and a parallel distributed compensation (PDC) scheme, we give stabilization conditions for closed-loop fuzzy systems with parametric uncertainties. Second, all the conditions are formulated in the format of linear matrix inequalities (LMIs) and contain upper bounds of the time derivative of premise membership functions as LMI variables. Finally, the T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. A numerical example of the chaotic Lorenz system is given to illustrate the utility of the fuzzy Lyapunov function approach.

Takagi-Sugeno (TS) fuzzy models have been the popular choice for multi-model based nonlinear system identification for controller design. However, the interpretation of the model from a dynamical systems point of view is still unclear. In this paper, we investigate the interpretation of the TS fuzzy models in terms of local dynamics of nonlinear systems in state space. The investigation is based on the comparison between the constant-affine recursive i/o equation and constant-affine state space representations. We show that the true local dynamics is not identifiable by TS fuzzy models by analysis and example. For the identification of constant-affine state space models, a subspace identification algorithm is proposed to identify the true local dynamics with zero initial conditions.

SummaryIn this paper, we develop a new model reference control architecture to effectively suppress system uncertainties and achieve a guaranteed transient and steady‐state system performance. Unlike traditional robust control frameworks, only a parameterization of the system uncertainty given by unknown weights with known conservative bounds is needed to stabilize uncertain dynamical systems with predictable system performance. In addition, the proposed architecture's performance is not dependent on the level of conservatism of the bounds of system uncertainty. Following the same train of thought as adaptive controllers that modify a given reference system to improve system performance, the proposed method is inspired by a recently developed command governor theory that minimizes the effect of system uncertainty by augmenting the input signal of the uncertain dynamical and reference systems. Specifically, a dynamical system, called a command governor, is designed such that its output is used to modify the input of both the controlled uncertain dynamical and reference systems. It is theoretically shown that if the command governor design parameter is judiciously selected, then the controlled system approximates the given original, unmodified reference system. The proposed approach is advantageous over model reference adaptive control approaches because linearity of the uncertain dynamical system is preserved through linear control laws, and hence, the closed‐loop performance is predictable for different command spectrums. Additionally, it is shown that the architecture can be modified for robustness improvements with respect to high frequency content due to, for example, measurement noise. Modifications can also be made in order to accommodate actuator dynamics and retain closed‐loop stability and predictable performance. The main contribution of this paper is the rigorous analysis of the stability and performance of a system utilizing the command governor framework. A numerical example is provided to illustrate the effectiveness of the proposed architecture. Copyright © 2015 John Wiley &amp; Sons, Ltd.

A direct hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework guarantees attraction of the closed-loop system states associated with the hybrid plant states in the face of parametric system uncertainty. A numerical example is provided to demonstrate the efficacy of the proposed approach.

This paper proposes the robust fuzzy fault tolerant control (FTC) problem for the fuzzy Takagi-Sugeno (TS) systems with sensor faults and actuator faults in the presence of parameter uncertainties. The TS fuzzy model is first employed to approximate a nonlinear uncertain system, and then the fuzzy sensor fault, fuzzy actuator fault model and the fuzzy state observer are developed. Sufficient stabilization conditions of the fuzzy FTC systems are given, which are formulated in terms of linear matrix inequalities (LMIs). The LMIs can be efficiently solved using the convex optimization techniques. Finally, fuzzy observer based on fuzzy fault tolerant controller is developed. It is proved that the fuzzy control system is reliable in the sense of that the closed-loop system is asymptotic stability and the all sensor and actuator components can operate well in the presence of some component failures. The control scheme is tested for real profiles of wind speed pattern and provides satisfactory results

This study presents a sum-of-squares (SOS) approach to stable control and guaranteed cost control of discrete polynomial fuzzy systems. The SOS framework presented in this paper offers a new paradigm over the existing linear matrix inequality (LMI) approaches to discrete Takagi-Sugeno (T-S) fuzzy models. At first, this study, newly introduces a discrete polynomial fuzzy model that is more general and effective than the well-known discrete T-S fuzzy model. With considering the operating domain, stable control design conditions are then derived based on state-dependent Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the design approach discussed in this study could be more general than the LMI design approaches based on quadratic Lyapunov functions. Moreover, this study also discusses a guaranteed cost control design which is carried out by minimising the upper bound of a given performance function. All the design conditions derived in this study can be represented in terms of SOS and are symbolically and numerically solved via the SOSOPT and the SeDuMi, respectively. Finally, the ball-and-beam system is provided as an example to illustrate the utility of the proposed SOS-based design approach.

This paper designs a preview repetitive control (PRC) policy for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and external disturbances. First, the T–S fuzzy model is employed to represent a nonlinear plant, once the nonlinear plant is represented by a T–S fuzzy model, a fuzzy improved-equivalent-input-disturbance (IEID)-based PRC law can be designed to achieve better tracking performance and disturbance rejection. Next, based on a new equality constraint, we derive a continuous-discrete two-dimensional (2D) system that paves the way to solve the design problem of the IEID-based PRC law using linear matrix inequality (LMI) approach. Then, by solving LMIs, the gains of the controller and state observer can be obtained. Finally, a numerical example is included to show the effectiveness of the proposed method.

This paper proposed a method of improved genetic algorithm (IGA)-based secure communications in multiple time delay chaotic (MTDC) systems with optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance and advanced encryption standard (AES). First, we apply an initial round key via AES encryption function to acquire the encrypted message. The encrypted message is used to carry out double encryption by chaotic synchronization. A robust fuzzy control design is then presented to address the effects of modeling errors between the MTDC systems and Takagi-Sugeno (T-S) fuzzy models. Next, in terms of Lyapunov's direct method, a delay dependent exponential stability criterion is derived to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are transformed into linear matrix inequalities (LMIs). In addition, the genetic algorithm (GA) has drawn great attention from researchers due to the capability of GA in random search for achieving near-optimal solutions. The lower and upper bounds of the search space based on the LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers in order to speed up the synchronization. However, the GA has the shortcomings of premature convergence and local search. Therefore, an improved genetic algorithm (IGA) is proposed in this study to effectively overcome the weakness of the traditional GA. On the basis of the IGA, a fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.

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.