Novel adaptive feedback synchronization scheme for a class of chaotic systems with and without parametric uncertainty

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).

SUMMARYThis paper presents an adaptive trajectory tracking controller for a non-holonomic wheeled mobile robot (WMR) in the presence of parametric uncertainty in the kinematic and dynamic models of the WMR and actuator dynamics. The adaptive non-linear control law is designed based on input–output feedback linearization technique to get asymptotically exact cancellation for the uncertainty in the given system parameters. In order to evaluate the performance of the proposed controller, a non-adaptive controller is compared with the adaptive controller via computer simulation results. The results show satisfactory trajectory tracking performance by virtue of SPR-Lyapunov design approach. In order to verify the simulation results, a set of experiments have been carried out on a commercial mobile robot. The experimental results also show the effectiveness of the proposed controller.

To maintain the vibrations of the gyroscope proof mass, an adaptive super-twisting sliding mode control (STSMC) of a micro gyroscope based on a two-loop recursive fuzzy neural network (TLRFNN) is designed. In order to estimate the unknown parameters of the nonlinear system online, an adaptive technology is adopted based on the parameter linearization of the nonlinear model. In response to the problem of system chattering caused by ordinary sliding mode control, the STSMC with the advantages of high order sliding mode and conventional sliding mode is introduced. Aiming at the problem of uncertainty in system parameters, a two-loop recursive fuzzy neural network approximation with the competence over the storage of a priori information is utilized. All adaptive laws are obtained under the Lyapunov stability framework which contributes to the stability of the system. The simulation research shows the system exhibits good tracking performance and maintains a small tracking error under the control of the suggested control system. The effect is measured by calculating the root mean square error (RMSE) parameter of the tracking error and the proposed control system achieves a tracking effect of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{1}}{\ ext{0.8590}} \ imes {\ ext{1}}{{\ ext{0}}^{ - 4}}$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{2}}{\ ext{0.0831}} \ imes {\ ext{1}}{{\ ext{0}}^{ - 4}}$$\\end{document} in the x and y directions, respectively.

In this paper, observer based synchronization of chaotic Lorenz system is presented. The virtual system concept is used for synchronization of observer states to actual system states. First, synchronization is presented without any uncertainty in system parameters and further synchronization is achieved for the case with uncertainty in system parameters. Adaptation law for uncertain parameters are developed as a consequence of stability analysis. Convergences of uncertain parameters are also analyzed. Simulation results are presented in the end to verify the synchronization of observer states to actual system states.

This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of synchronization and anti-synchronization between different chaotic systems with fully uncertain parameters and different structure are studied. Based on the Lyapunov stability theory, a novel, simple, and systemic adaptive synchronization controller is designated, the analytic expression of the controller and the adaptive laws of parameters are developed. Moreover, the proposed scheme can be extended to anti-synchronize a class of chaotic systems. Two chaotic systems with different structure and fully uncertain parameters are employed as the examples to show the effectiveness of the proposed adaptive synchronization and anti-synchronization schemes. Additionally, the robustness and noise immunity of the adaptive synchronization scheme is investigated by measuring the mean squared error of the systems.

Adaptive Backstepping Control for A Twin Rotor MIMO System

The present study aims to design a robust adaptive controller employed in the active tuned mass damper (ATMD) system to overcome undesirable vibrations in multistory buildings under seismic excitations. We propose a novel adaptive type-2 neural-fuzzy controller (AT2NF). All system parameters are taken as unknowns. The MLP neural network is used to extract the Jacobian and estimate the structural model; then, the estimated model is applied to the controller online. To tune the control force applied to the ATMD and achieve the control targets, the controller parameters are adaptively trained using the extended Kalman Filter (EKF) and the error back-propagation algorithm. A PID controller is also included in this method to increase the stability and robustness of the adaptive type-2 neural-fuzzy controller against seismic vibrations. An online simple adaptive controller (OSAC) is studied to demonstrate the suggested controller's superiority. The OSAC is based on adaptive control of the implicit reference model. In this proposed method, the EKF is used to tune the controller parameters online as a novel feature. The uncertainty associated with identifying the mechanical properties of structures, such as mass and stiffness, is one of the primary challenges in the real-time control of structures. This paper investigates how both controllers cope with parametric uncertainties under far-field and near-field seismic excitation. According to numerical results, the AT2NF controller outperforms OSAC in minimizing the dynamic responses of the structure during an earthquake and accomplishing control objectives when the structure's characteristics change.

Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation

The negative impacts of microgrids (µGs) on the load frequency highlight the importance of implementing a robust, efficient, and adaptable controller to ensure stability. This work introduces an adaptive load frequency control (LFC) for an isolated µG that includes a PV system and electric vehicles (EVs), which have a significant impact on frequency. This control utilizes a combination of sine cosine optimization (SCO) and balloon effect identifier (BEI) algorithms. The controller presented in this work transforms the LFC process into an optimization problem that is highly compatible with various random situations encountered in the control process. The suggested control method is a novel approach by utilizing SCO+BEI for adaptive LFC application, resulting in a highly efficient response. The effectiveness of the proposed adaptive controller is assessed under the conditions of 17 MW variable load, system parameters uncertainties, and installed PV systems of 6 MW. MATLAB / Simulink package is rummage-sale as a digital test environment. According to simulation results, the proposed adaptive controller succeeds in regulating the frequency and power of an islanded µG. To measure the efficiency of the proposed control scheme, a comparison between other control techniques (such as adaptive controller using Jaya+BEI and classical integral controller) is done. The findings of the studied scenarios assured that the not compulsory control method using (SCO+BEI) has an obvious superiority over other control methods in terms of frequency solidity in case of random load instabilities and parameter uncertainties. Finally, it can be said that the proposed controller can better ensure the safe operation of the µGs.

Recently, a new six-term 3-D chaotic system with an exponential nonlinearity was discovered (Sundarapandian, 2013). This novel chaotic system has two saddle focus nodes and hence they are unstable. The maximal Lyapunov exponent (MLE) for the six-term Sundarapandian chaotic system was found as 3.2827 and the Lyapunov dimension of the Sundarapandian chaotic system was found as D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> = 2.1668. Complete synchronization of chaotic systems deals with the problem of asymptotically synchronizing the states of a pair of chaotic systems called as master and slave systems with the help of controllers attached to the slave system. Complete synchronization of chaotic systems has applications in many engineering areas such as secure communications, secure data encryption, cryptosystems, etc. This paper addresses the design of active and adaptive feedback controllers for completely synchronizing the states of identical six-term Sundarapandian chaotic systems with exponential nonlinearity. Active controllers are used when the system parameters a, b and c are available for measurement and the synchronization result is established using Lyapunov stability theory. Numerical simulations using MATLAB have been shown to demonstrate the proposed active and adaptive synchronization results for the novel chaotic system discussed in this paper.

In this note, we propose a unified framework for adaptive iterative learning control design for uncertain nonlinear systems. It is shown that if a Lyapunov based adaptive control law is available for the system under consideration and the Lyapunov function satisfies certain conditions, it is straightforward to extend the adaptive controller to handle repetitive systems operating over a finite time interval. According to the value of a certain parameter γ, the parametric adaptation law can be a pure time-domain adaptation, a pure iteration-domain adaptation or a combination of both.A pure iteration-domain adaptation is described by a difference equation, a pure time-domain adaptation is described by a differential equation, and a combination of both is described by a differential-difference equation. The advantages and disadvantages of the three possible adaptation types are discussed and some illustrative examples are given.

Adaptive control has been developed for decades, and now it has become a rigorous and mature discipline which mainly focuses on dealing parametric uncertainties in control systems, especially linear parametric systems. Nonparametric uncertainties were seldom studied or addressed in the literature of adaptive control until new areas on exploring limitations and capability of feedback control emerged in recent years. Comparing with the approach of robust control to deal with parametric or nonparametric uncertainties, the approach of adaptive control can deal with relatively larger uncertainties and gain more flexibility to fit the unknown plant because adaptive control usually involves adaptive estimation algorithms which play role of “learning” in some sense. This chapter will introduce a new challenging topic on dealing with both parametric and nonparametric internal uncertainties in the same system. The existence of both two kinds of uncertainties makes it very difficult or even impossible to apply the traditional recursive identification algorithms which are designed for parametric systems. We will discuss by examples why conventional adaptive estimation and hence conventional adaptive control cannot be applied directly to deal with combination of parametric and nonparametric uncertainties. And we will also introduce basic ideas to handle the difficulties involved in the adaptive estimation problem for the system with combination of parametric and nonparametric uncertainties. Especially, we will propose and discuss a novel class of adaptive estimators, i.e. information-concentration (IC) estimators. This area is still in its infant stage, and more efforts are expected in the future for gainning comprehensive understanding to resolve challenging difficulties. Furthermore, we will give two concrete examples of semi-parametric adaptive control to demonstrate the ideas and the principles to deal with both parametric and nonparametric uncertainties in the plant. (1) In the first example, a simple first-order discrete-time nonlinear system with both kinds of internal uncertainties is investigated, where the uncertainty of non-parametric part is characterized by a Lipschitz constant L, and the nonlinearity of parametric part is characterized by an exponent index b. In this example, based on the idea of the IC estimator, we construct a unified adaptive controller in both cases of b = 1 and

A passivity-based adaptive control law is presented, which transforms the permanent magnet synchronous motor (PMSM) with v/f controller into an equivalent passive system. It is proved that the equivalent system can be asymptotically stabilized at different equilibrium points without any influence of undeterministic parameters. Simulation results show the proposed control law is very effective and robust against the uncertainty in system parameters.

Adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with dead-zone inputs

SummaryAdaptive control schemes are developed for uncertain multivariable systems with unmatched input disturbances and are applied to an aircraft flight turbulence compensation problem. Key relative degree conditions from system input and disturbance are derived in terms of system interactor matrices for the design of a nominal state or output feedback control law that ensures desired asymptotic output tracking and disturbance rejection. To deal with an uncertain system high‐frequency gain matrix, a gain matrix decomposition technique is employed to parametrize an error system model in terms of the parameter and tracking errors, for the design of an adaptive parameter update law with reduced system knowledge. Both adaptive state and output feedback control schemes are presented in detail for systems with general interactor matrices, based on an LDS gain decomposition parametrization, and LDU and SDU decomposition‐based designs are also discussed, to develop unified adaptive disturbance rejection techniques for multivariable systems. All closed‐loop system signals are bounded, and the system output tracks a reference output asymptotically despite the system and disturbance parameter uncertainties. Simulation results of an aircraft flight control system with adaptive turbulence compensation are presented to show the desired system disturbance rejection performance. Copyright © 2015 John Wiley &amp; Sons, Ltd.