Design of a multilevel fuzzy controller for nonlinear systems and stability analysis

In this paper, a multilevel fuzzy control (MLFC) system is developed and implemented to deal with the real-world nonlinear plants with intrinsic uncertainties and time-varying parameters. The proposed fuzzy control strategy has a hierarchical structure with an adaptation mechanism embedded in the lower level to tune the output membership functions (MFs) of the first layer fuzzy controller and can be used to control a system with an input-output monotonic relationship or a piecewise monotonic relationship. The stability of the closed-loop system under the proposed MLFC is theoretically proven. Simulations are carried out by applying the proposed multilevel fuzzy control (MLFC) to a uncertain nonlinear plants, and it is shown that much better system performances are achieved compared with conventional fuzzy logic controllers (FLC), even in presence of disturbance and noise.     

基于KQ的航空发动机多变量控制算法研究

针对某型双转子、双涵道混合排气式涡扇发动机多变量控制系统要求,首先以相关增益矩阵方法研究了航空发动机多变量控制方案中的被控参数与控制量的一一对应关系问题,然后阐明了KQ算法的基本原理和基本算法,并以飞行条件为H=11 km、Ma =1.2为仿真算例点,设计了基于KQ算法的多变量控制器.与非线性部件级气动热力学模型组成控...     

Fuzzy control of multivariable nonlinear servomechanisms withexplicit decoupling scheme

This paper deals with the problem of controlling multivariable nonlinear servomechanisms by means of fuzzy approaches. A specific system under consideration is a passive nonlinear line-of-sight (LOS) stabilization system with strong interactions between two channels. By using the concept of decentralized control, a control structure is developed that is composed of two control loops, each of which is associated with a single-variable fuzzy controller and a decoupling unit. A simplified fuzzy control algorithm is used to implement the fuzzy controller. We propose two novel approaches to designing the decoupling units. The first one is based on the theory of fuzzy reasoning whereas the second scheme relies on the principle of adaptation. Extensive simulation studies on the LOS system have demonstrated the feasibility and effectiveness of the proposed approach     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

未知多变量非线性系统自适应模糊预测控制

对一类未知多变量非线性系统提出了直接自适应模糊预测控制方法,此方法首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直接用模糊逻辑系统组成的向量来设计预测控制器,并基于时变死区函数对控制器中的未知向量和广义误差估计值中的未知矩阵进行自适应调整．文中证明了此方法可使广义误差向量估计值收敛到原点的一个邻域内．     

Fuzzy adaptive modular design of uncertain chaotic Duffing oscillators

This paper proposes a fuzzy adaptive control approach based on a modular design for uncertain chaotic Duffing oscillators. Using fuzzy logic, the unknown nonlinear function in the Duffing oscillator is approximated. Subsequently, a modular adaptive controller is derived consisting of an inputtostate stabilizing (ISS) control module and a passive identifier module. Since the modular design allows for independent design of the controller and identifier, the proposed method provides substantial flexibility in the choice of a parameter identifier. Additionally, the modularity of the controller-identifier pair provides simplicity in the control system derivation. Simulation results are included to illustrate the effectiveness of the proposed approach.     

Direct adaptive fuzzy control for nonlinear systems with time-varying delays

This paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict-feedback systems with time-varying delays. Based on the Razumikhin function approach, a novel adaptive fuzzy controller is designed. The proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. Different from the existing adaptive fuzzy control methodology, the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems. As a result, the proposed adaptive controller has a simpler form and requires fewer adaptation parameters.     

一类多变量非线性系统的自适应模糊控制

针对一类具有干扰和不确定性的多变量非线性系统, 提出了一种自适应模糊控制方法. 该多变量系统由 m 个互连子系统组成, 每个互连子系统中的未知函数是非仿射的. 由于不确定非仿射函数的存在和互连子系统之间的耦合, 这类系统是很难控制的. 通过利用均值定理、模糊系统、Backstepping 设计方法以及引入 Nussbaum 类型函数, 克服了这个困难. 另外, 与大多数研究结果相比较, 提出的方法减少了在线调节参数的数量. 提出的控制方法能实现闭环系统的所有信号是有界的. 仿真实验表明该控制方法的有效性.     

Adaptive neural/fuzzy control for interpolated nonlinear systems

Adaptive control for nonlinear time-varying systems is of both theoretical and practical importance. We propose an adaptive control methodology for a class of nonlinear systems with a time-varying structure. This class of systems is composed of interpolations of nonlinear subsystems which are input-output feedback linearizable. Both indirect and direct adaptive control methods are developed, where the spatially localized models (in the form of Takagi-Sugeno fuzzy systems or radial basis function neural networks) are used as online approximators to learn the unknown dynamics of the system. Without assumptions on rate of change of system dynamics, the proposed adaptive control methods guarantee that all internal signals of the system are bounded and the tracking error is asymptotically stable. The performance of the adaptive controller is demonstrated using a jet engine control problem.     

Adaptive control of MIMO time-varying systems with indicator function based parametrization

This paper studies a new solution framework for adaptive control of a class of MIMO time-varying systems with indicator function based parametrization, motivated by a general discrete-time MIMO Takagi–Sugeno (T–S) fuzzy system model in an input–output form with unknown parameters. An indicator (membership) function based parametrization has some favorable capacity to deal with certain large parameter variations. A new discrete-time MIMO system prediction model is derived for approximating a nonlinear dynamic system, and its system properties are clarified. An adaptive control scheme is developed, with desired controller parametrization and stable parameter estimation for control of such uncertain MIMO time-varying systems. A control singularity problem is addressed and the closed-loop stability and output tracking properties are analyzed. This work provides a new method for multivariable T–S fuzzy system modeling and adaptive control. An illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance.     

A new T-S fuzzy model predictive control for nonlinear processes

In this paper, a novel fuzzy Generalized Predictive Control (GPC) is proposed for discrete-time nonlinear systems via Takagi-Sugeno system based Kernel Ridge Regression (TS-KRR). The TS-KRR strategy approximates the unknown nonlinear systems by learning the Takagi-Sugeno (TS) fuzzy parameters from the input-output data. Two main steps are required to construct the TS-KRR: the first step is to use a clustering algorithm such as the clustering based Particle Swarm Optimization (PSO) algorithm that separates the input data into clusters and obtains the antecedent TS fuzzy model parameters. In the second step, the consequent TS fuzzy parameters are obtained using a Kernel ridge regression algorithm. Furthermore, the TS based predictive control is created by integrating the TS-KRR into the Generalized Predictive Controller. Next, an adaptive, online, version of TS-KRR is proposed and integrated with the GPC controller resulting an efficient adaptive fuzzy generalized predictive control methodology that can deal with most of the industrial plants and has the ability to deal with disturbances and variations of the model parameters. In the adaptive TS-KRR algorithm, the antecedent parameters are initialized with a simple K-means algorithm and updated using a simple gradient algorithm. Then, the consequent parameters are obtained using the sliding-window Kernel Recursive Least squares (KRLS) algorithm. Finally, two nonlinear systems: A surge tank and Continuous Stirred Tank Reactor (CSTR) systems were used to investigate the performance of the new adaptive TS-KRR GPC controller. Furthermore, the results obtained by the adaptive TS-KRR GPC controller were compared with two other controllers. The numerical results demonstrate the reliability of the proposed adaptive TS-KRR GPC method for discrete-time nonlinear systems.     

Adaptive fuzzy decentralised control for stochastic nonlinear large-scale systems in pure-feedback form

This paper is concerned with the problem of adaptive fuzzy decentralised output-feedback control for a class of uncertain stochastic nonlinear pure-feedback large-scale systems with completely unknown functions, the mismatched interconnections and without requiring the states being available for controller design. With the help of fuzzy logic systems approximating the unknown nonlinear functions, a fuzzy state observer is designed estimating the unmeasured states. Therefore, the nonlinear filtered signals are incorporated into the backstepping recursive design, and an adaptive fuzzy decentralised output-feedback control scheme is developed. It is proved that the filter system converges to a small neighbourhood of the origin based on appropriate choice of the design parameters. Simulation studies are included illustrating the effectiveness of the proposed approach.     

Direct adaptive fuzzy control of a class of MIMO non-affine nonlinear systems

An adaptive fuzzy control approach is proposed for a class of multiple-input–multiple-output (MIMO) nonlinear systems with completely unknown non-affine functions. The global implicit function theorem is first used to prove the existence of an unknown ideal implicit controller that can achieve the control objectives. Within this scheme, fuzzy systems are employed the approximate the unknown ideal implicit controller, and robustifying control terms are used to compensate the approximation errors and external disturbances. The adjustable parameters of the used fuzzy systems are deduced from the stability analysis of the closed-loop system in the sense of Lyapunov. To show the efficiency of the proposed controllers, two simulation examples are presented.     

A self-tuning regulator for multivariable systems

The controller described in this paper is designed for multivariable plants with constant, unknown parameters. The algorithm operates on-line with the a priori information about the time delay. The order of the system may be given a priori. In the case where the order of the system is unknown it can be determined by a generalized likelihood-ratio statistical test which is described in this paper. The multivariable self tuning regulator consists of the two tasks of estimation and regulation. Estimation of the input-output system model parameters is based on the least-squares principle. The control is computed to minimize the combined cost of output deviation and control energy. Asymptotic properties of the estimation are discussed. Usefulness and simplicity of this approach are illustrated by examples.     

Stable fuzzy neural tracking control of a class of unknown nonlinear systems based on fuzzy hierarchy error approach

In this paper, a stable fuzzy neural tracking control of a class of unknown nonlinear systems based on the fuzzy hierarchy approach is proposed. The adaptive fuzzy neural controller is constructed from the fuzzy neural network with a set of fuzzy rules. The corresponding network parameters are adjusted online according to the control law and update law for the purpose of controlling the plant to track a given trajectory. A stability analysis of the unknown nonlinear system is discussed based on the Lyapunov principle. In order to improve the convergence of the nonlinear dynamical systems, a fuzzy hierarchy error approach (FHEA) algorithm is incorporated into the adaptive update and control scheme. The simulation results for an unstable nonlinear plant demonstrate the control effectiveness of the proposed adaptive fuzzy neural controller and are consistent with the theoretical analysis.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

一类非线性系统的积分变结构模糊自适应跟踪控制

针对一类具有未知常数控制增益的不确定非线性系统,基于变结构控制原理,并利用具有非线性可调参数的模糊系统逼近等价控制,提出一种具有监督控制器的积分变结构模糊自适应跟踪控制策略.该策略通过监督控制器保证闭环系统所有信号有界.进一步,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响.理论分析证明了跟踪误差能够收敛到零.仿真结果表明了该方法的有效性.     

多变量非线性系统参数自调整的模糊加权控制

本文针对多变量非线性系统,提出了一种参数自调整的模糊加权信息融合方法．利用 模糊组合变量降低模糊控制系统的维数,根据不同的模糊组合变量对最后决策的作用大小, 赋予不同的权重来实现对多变量非线性系统的控制,在利用反向传播算法对量化系数和加权 系数进行自学习后,在线进行基于模糊规则的参数自调整,有效地解决了多变量模糊控制系 统中难于设计多维规则库和在线实现自适应模糊控制的问题．本文还对所提出的方法进行了 仿真实验和实际系统的实验,实验结果证明了该方法的有效性．     

未知非线性系统自适应改进RBF滑模控制

针对一类未知的非线性系统,利用输入/输出线性化将其变换为部分线性可控系统,通过RBF神经网络对未知非线性函数进行逼近,提出了一种基于RBF神经网络的自适应滑模控制,并设计了自适应滑模控制器;提出了一种连续函数,很好地减少了抖振现象,使得闭环系统状态一致稳定最终有界。实验结果验证了方法的有效性。