Optimal and stable fuzzy controllers for nonlinear systems based on an improved genetic algorithm

This paper addresses the optimization and stabilization problems of nonlinear systems subject to parameter uncertainties. The methodology is based on a fuzzy logic approach and an improved genetic algorithm (GA). The TSK fuzzy plant model is employed to describe the dynamics of the uncertain nonlinear plant. A fuzzy controller is then obtained to close the feedback loop. The stability conditions are derived. The feedback gains of the fuzzy controller and the solution for meeting the stability conditions are determined using the improved GA. In order to obtain the optimal fuzzy controller, the membership functions are further tuned by minimizing a defined fitness function using the improved GA. An application example on stabilizing a two-link robot arm will be given.     

On the robustness of stability for uncertain large-scale systems subjected to multiple time delays

The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.Notation real number field - complex number field - x x=(x ₁,x ₂,...,x _n ) ^T R ⁿ - x ^T transpose of vectorx - x* complex conjugate transpose of vectorx - Re(·) real part of (·) - x norm of vectorx; x=(x*x)^1/2 - A ^T transpose of matrixA - A* complex conjugate transpose of matrixA - ¯(·) maximal absolute value of eigenvalue of matrixA - (A) matrix measure of matrixA; (A)=¯((A + A*)/2) - A induced norm of matrix A; A=[¯(A*A)]^1/2 - ¦a_ij ¦ absolute value of element a_ij - ¦ A¦ {¦a_ij¦} for matrix A={a_ij} - A >B a_ij > b_ij for alli andj where A={a_ij} andB={b_ij} - z complex number - ¯z complex conjugate ofz Supported by National Science Council, Taiwan, Republic of China, Grant NSC83-0404-E006-001.     

A fuzzy sliding controller for nonlinear systems

It is well known that sliding-mode control can give good transient performance and system robustness. However, the presence of chattering may introduce problems to the actuators. Many chattering elimination methods use a finite DC gain controller which leads to a finite steady-state error. One method to ensure zero steady-state error is using a proportional plus integral (PI) controller. This paper proposes a fuzzy logic controller which combines a sliding-mode controller (SMC) and a PI controller. The advantages of the SMC and the PI controller can be combined and their disadvantages can be removed. The system stability is proved, although there is one more state variable to be considered in the PI subsystem. An illustrative example shows that good transient and steady-state responses can be obtained by applying the proposed controller     

Multiple time scales for nonlinear systems

In this paper we extend the results on the multiple time-scale structure for linear autonomous systems of the form $$\dot x = A( \in )x$$ (cf. Coderchet al. [1]) to nonlinear autonomous systems. Our main result is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure.     

Transient and frequency responses of systems with time delays

For systems containing time delays, root locus methods can locate any Laplace transform closed-loop poles. L'H?pital's rule is shown to give exact residue values for any of the infinity of closed-loop poles. The transient or frequency response can then be estimated from dominant poles and their residues.     

Analysis of nonlinear systems with multiple inputs

Analytical modeling of communication receivers to account for their nonlinear response to multiple input signals is discussed. The method is based on the application of the Wiener-Volterra analysis of nonlinear functionals. The derived analytical relations were embodied in a computer program which provides nonlinear transfer functions of large circuits specified by their parameters. This method was applied to the prediction of behavior of communication receivers in the presence of interference. Examples illustrate the method and demonstrate its validity in the small-signal region.     

Synthesis of linear optimum distributed parameter systems with time delays

A variational calculus approach is used to study quadratic optimization of linear time-delayed distributed parameter systems with distributed and boundary control function. The canonical equations are derived for the necessary condition of optimality. Then the Riccati equations are obtained and their computational solution is discussed.     

Measurement of time delays in multipath systems

In a recent letter, Gouriet proposed a method of measuring time delay, which uses the fact that the time delay of a linear system is the group delay at zero frequency. Based on the same method, a system is proposed in this letter to measure the time delays in a linear system which provides more than one transmission path between a single output and a single input. The system assumes that a rough knowledge of the magnitudes of time delays is available and that the individual multipath responses do not overlap in the time domain.     

Global robust stability analysis of neural networks with multiple time delays

Global robust convergence properties of continuous-time neural networks with discrete delays are studied. By employing suitable Lyapunov functionals, we derive a set of delay-independent sufficient conditions for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point. The conditions can be easily verified as they can be expressed in terms of the network parameters only. Some numerical examples are given to compare our results with previous robust stability results derived in the literature. One of our main results is shown to improve and generalize a previously published result. Other results proved to establish a new set of robust stability criteria for delayed neural networks.     

Stability of nonlinear systems with three time scales

We study the asymptotic stability of a singularly perturbed nonlinear time-invariant systemS _v , which has three vastly different time scales. The systemS _v is approximated by three simpler systems over different time intervals. We give a straightforward proof of the fact that the asymptotic stability ofS _v is guaranteed when the equilibrium points of the three simpler systems are exponentially stable and when the parameters and are sufficiently small.Research sponsored by the Joint Services Electronics Program, Contract Number F4962084-C-0057, and NASA, Grant NAG2-243.     

Global stability of Internet congestion controllers with heterogeneous delays

In this paper, we study the problem of designing globally stable, scalable congestion control algorithms for the Internet. Prior work has primarily used linear stability as the criterion for such a design. Global stability has been studied only for single node, single source problems. Here, we obtain conditions for a general topology network accessed by sources with heterogeneous delays. We obtain a sufficient condition for global stability in terms of the increase/decrease parameters of the congestion control algorithm and the price functions used at the links.     

Stabilisation of closed loop systems by time delays

It is generally recognised that time delays will cause closed loop systems to become unstable. The adverse effect on stability caused by time delays is presented. Bounds on time delays for the stabilisation of unstable closed loop systems are also derived.<>     

Multilayered fuzzy behavior fusion for real-time reactive controlof systems with multiple sensors

Fuzzy linguistic rules provide an intuitive and powerful means for defining control behavior. Most applications that use fuzzy control feature a single layer of fuzzy inference, mapping a function from one or two inputs to equally few outputs. Highly complex systems, with large numbers of inputs, may also benefit from the use of qualitative linguistic rules if the control task is properly partitioned. This paper presents a modular fuzzy control architecture and inference engine that can be used to control complex systems. The control function is broken down into multiple local agents, each of which samples a subset of a large sensor input space. Additional fuzzy agents are employed to fuse the recommendations of the local agents. Real-time implementation without special hardware is possible by using singleton output values during fuzzy rule evaluation. A development tool is used to translate a fuzzy programming language offline for fast execution at run time. Using this system, a multilayered fuzzy behavior fusion based reactive control system has been implemented on an autonomous mobile robot, MARGE, with great success. MARGE won first place in Event III of the 1993 Robot Competition sponsored by the American Association for Artificial Intelligence     

Decentralized variable structure control of interconnected multi-input/ multi-output nonlinear systems

For a broad class of interconnected nonlinear systems, this paper develops a complete design methodology for decentralized variable structure control. Specifically, the paper sets forth design schemes for local switching surfaces and the related local switched feedback gains which together force the original nonlinear interconnected system to behave as a reduced order interconnected equivalent system having a desired response such as stability, tracking, or prespecified eigenvalues. Also developed is a numerical algorithm for constructing the switched local feedback gains. A simple nonlinear example illustrates the control strategy.     

Delay-dependent robust H_\infty control for 2-D discrete nonlinear systems with state delays

This paper investigates the problem of robust \(H_\infty \) control for a class of 2-D (two-dimensional) discrete state delayed systems with sector nonlinearity described by a model of Roesser type. Firstly, a delay-dependent sufficient condition of robust exponential stability for such 2-D discrete systems is derived in linear matrix inequalities (LMIs) form. Secondly, a delay-dependent exponential stability criterion with \(H_\infty \) performance for the considered systems is also proposed. Then a state feedback \(H_\infty \) controller is constructed based on the above results. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

多时滞Lurie网络控制系统动态输出反馈控制器设计

针对一类具有非理想网络状况,如时变网络时滞、分组丢失和乱序等问题的基于动态输出反馈控制器的网络控制系统,建立了多时滞Lurie网络控制系统模型,应用Lyapunov-Krasovskii泛函方法,保留Lyapunov-Krasovskii泛函导数中经常被忽略的有用项,提出了一种具有更低保守性的多时滞Lurie网络控制系统时滞相关稳定条件。并通过增加一等式约束将非线性矩阵不等式转化为线性矩阵不等式表示的可解性问题,给出了一种动态输出反馈控制器的设计方法。数值实例表明该设计方法具有更低的保守性。     

Separation of multiple time delays using new spectral estimationschemes

The problem of estimating multiple time delays in presence of colored noise is considered. This problem is first converted to a high-resolution frequency estimation problem. Then, the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure. These matrices are shown to be as effective in extracting bases for the signal and noise subspaces as the standard autocorrelation matrix, which is normally used in MUSIC and the pencil-based methods. Frequency estimators are then derived using these subspaces. The effectiveness of the method is demonstrated on two examples: a standard frequency estimation problem in presence of colored noise and a real-world problem that involves separation of multiple specular components from the acoustic backscattered from an underwater target     

Vision-based nonlinear tracking controllers with uncertainrobot-camera parameters

This paper considers the problem of position tracking control of planar robot manipulators via visual servoing in the presence of parametric uncertainty associated with the robot mechanical dynamics and/or the camera system. Specifically, by assuming exact knowledge of the mechanical parameters, we design an adaptive camera calibration controller that compensates for uncertain camera parameters and ensures global asymptotic position tracking. We then develop an adaptive robot controller that accounts for parametric uncertainty throughout the entire robot-camera system while producing global asymptotic position tracking. Experimental results illustrating the viability of the adaptive controllers and extensions regarding robust control and redundant robot manipulators are also included     

Absolute stability of nonlinear control systems with time lag

A nonlinear control system with time lag is transformed into a nonlinear control system with no time lag by means of certain types of transformations. If absolute stability for this transformed nonlinear control system is obtained by Popov's method, absolute stability in the nonlinear control system with time lag is realized.     

Identification and tuning fractional order proportional integral controllers for time delayed systems with a fractional pole

First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the model with a single fractional pole replacing the integer order pole, which is believed to better characterize the reaction curve. In this paper, using time delayed system model with a fractional pole as the starting point, fractional order controllers design for this class of fractional order systems is investigated. Integer order PID and fractional order PI and [PI] controllers are designed and compared for these class of systems. The simulation comparison between PID controller and fractional order PI and [PI] controllers show the advantages of the properly designed fractional order controllers. Experimental results on a heat flow platform are presented to validate the proposed design method in this paper.