Chaotic synchronization via linear controller

A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively. This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.

STATE FEEDBACK STABILIZATION FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS VIA DYNAMIC LINEAR CONTROLLERS

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay.First,using the dynamic change of coordinates,the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions.With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates,the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller.The growth condition in perturbations are more general than that in the existing results.The correctness of the theoretical results are illustrated with an academic simulation example.

Robust H_∞ Stabilization of Uncertain Linear Time-Delay System with Delayed/Undelayed State Feedback Controllers

This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.

Trajectory tracking control based on linear active disturbance rejection controller for 6-DOF robot manipulator

The trajectory tracking control for a 6-DOF robot manipulator with multiple inputs and outputs,non-linearity and strong coupling is studied.Firstly,a dynamical model for the 6-DOF robot manipulator is designed.From the view point of practical engineering,considering the model uncertainties and external disturbances,the robot manipulator is divided into 6 independent joint subsystems,and a linear active disturbance rejection controller(LADRC)is developed to track trajectory for each subsystem respectively.LADRC has few parameters that are easy to be adjusted in engineering.Linear expansion state observer(LESO)as the uncertainty observer is able to estimate the general uncertainties effectively.Eventually,the validity and robustness of the proposed method adopted in 6-DOF robot manipulator are demonstrated via numerical simulations and 6-DOF robot manipulator experiments,which is of practical value in engineering application.

A new kind of nonlinear fractional-order chaotic phenomenon in coupled systems： coexistence of anti-phase and complete synchronization

In this paper, we have found a kind of interesting nonlinear phenomenon hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti- phase synchronized and part completely synchronized, can be achieved using a single linear controller with only one drive variable. Based on the stability theory of the fractional-order system, we investigated the possible existence of this new synchronization mechanism. Moreover, a helpful theorem, serving as a determinant for the gain of the controller, is also presented. Solutions of coupled systems are obtained numerically by an improved Adams Bashforth-Moulton algorithm. To support our theoretical analysis, simulation results are given.

Quaternion-based Nonlinear Trajectory Tracking Control of a Quadrotor Unmanned Aerial Vehicle

At present, most controllers of quadrotor unmanned aerial vehicles（UAVs） use Euler angles to express attitude. These controllers suffer a singularity problem when the pitch angle is near 90°, which limits the maneuverability of the UAV. To overcome this problem, based on the quatemion attitude representation, a 6 degree of freedom（DOF） nonlinear controller of a quadrotor UAV is designed using the trajectory linearization control（TLC） method. The overall controller contains a position sub-controller and an attitude sub-controller. The two controllers regulate the translational and rotational motion of the UAV, respectively. The controller is improved by using the commanded value instead of the nominal value as the input of the inner control loop. The performance of controller is tested by simulation before and after the improvement, the results show that the improved controller is better. The proposed controller is also tested via numerical simulation and real flights and is compared with the traditional controller based on Euler angles. The test results confirm the feasibility and the robustness of the proposed nonlinear controller. The proposed controller can successfully solve the singularity problem that usually occurs in the current attitude control of UAV and it is easy to be realized.

Trajectory linearization control of an aerospace vehicle based on RBF neural network

An enhanced trajectory linearization control （TLC） structure based on radial basis function neural network （RBFNN） and its application on an aerospace vehicle （ASV） flight control system are presensted. The influence of unknown disturbances and uncertainties is reduced by RBFNN thanks to its approaching ability, and a robustifying itera is used to overcome the approximate error of RBFNN. The parameters adaptive adjusting laws are designed on the Lyapunov theory. The uniform ultimate boundedness of all signals of the composite closed-loop system is proved based on Lyapunov theory. Finally, the flight control system of an ASV is designed based on the proposed method. Simulation results demonstrate the effectiveness and robustness of the designed approach.

Research of robust adaptive trajectory linearization control based on T-S fuzzy system

A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.

A hybrid multi-degree-of-freedom vibration isolation platform for spacecrafts by the linear active disturbance rejection control

The hybrid vibration isolation, which takes advantages of both the passive and active approaches, has been an important solution for space missions. The objective of this paper is to design a vibration isolation platform for payloads on spacecrafts with the robust, wide bandwidth, and multi-degree-of-freedom(MDOF). The proposed solution is based on a parallel mechanism with six voice-coil motors(VCMs) as the actuators. The linear active disturbance resistance control(LADRC) algorithm is used for the active control. Numerical simulation results show that the vibration isolation platform performs effectively over a wide bandwidth, and the resonance introduced by the passive isolation is eliminated. The system robustness to the uncertainties of the structure is also verified by simulation.

A new hyperchaotic system and its linear feedback control

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.

A nonlinear model reference adaptive inverse control algorithm with pre-compensator

In this paper, the reduced-order modeling （ROM） technology and its corresponding linear theory are expanded from the linear dynamic system to the nonlinear one, and H∞ control theory is employed in the frequency domain to design some nonlinear system＇ s pre-compensator in some special way. The adaptive model inverse control （AMIC）theory coping with nonlinear system is improved as well. Such is the model reference adaptive inverse control with pre-compensator （PCMRAIC）. The aim of that algorithm is to construct a strategy of control as a whole. As a practical example of the application, the nunlerical simulation has been given on matlab software packages. The numerical result is given. The proposed strategy realizes the linearization control of nonlinear dynamic system. And it carries out a good performance to deal with the nonlinear system.

Hybrid Predictive Control with Simple Linear Control Based Circulating Current Suppression for Modular Multilevel Converters

The modular multilevel converter(MMC)has become a promising topology for widespread power converter applications.However,an evident circulating current flowing between the phases will increase system losses and complicate the heatsink design.This paper proposes a novel hybrid model predictive control method for MMCs.This method utilizes an indirect structure MPC and a sorting algorithm to implement current tracking and capacitor voltages balancing,considerably resulting in reduced calculation burden.In addition,different from the conventional MPC solutions,we add a simple proportional-integral(PI)controller to suppress circulating current through modifying the submodule(SM)inserted number,which is parallel to the MPC loop.This hybrid control solution combines both advantages of MPC and linear control,evidently resulting in improved performance of circulating current.Finally,the MATLAB/Simulink results of an 11-level MMC system verify the effectiveness of the proposed solution.

New trajectory linearization control for nonlinear systems undergoing harmonic disturbance

This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and the phase are unknown. A disturbance observer dynamics is constructed to estimate the harmonic disturbance, and then the estimation is used to implement a compensation control law to cancel the disturbance. By Lyapunov＇s direct method, a rigorous poof shows that the composite error of the closed-loop system can approach zero exponentially. Finally, the proposed method is illustrated by the application to control of an inverted pendulum. Compared with two existing methods, the proposed method demonstrates better performance in tracking error and response time.

ROBUST CONTROL VIA STATE FEEDBACK FOR A CLASS OF UNCERTAIN BILINEAR SYSTEMS

This paper is concerned with the problem of designing a stabilizing controller for a class of uncertain bilinear systems. The uncertainties in the systems must satisfy the matching condition and their bounds should be known. The so-called improved approach for stability analysis of nonlinear system was used. Under some suitable assumptions a linear robust state feedback controller can be designed. At last, an illustrative example was demonstrated.

Linear Quadratic Integral Control for the Active Suspension of Vehicle

The quarter model of an active suspension is established in the form of controllable autoregressive moving average （CARMA） model. An accelerometer can be mounted on the wheel hub for measuring road disturbance; this signal is used to identify the CARMA model parameters by recursive forgetting factors least square method. The linear quadratic integral （LQI） control method for the active suspension is presented. The LQI control algorithm is fit for vehicle suspension control, for the control performance index can comprise multi controlled variables. The simulation results show that the vertical acceleration and suspension travel both are decreased with the LQI control in the low frequency band, and the suspension travel is increased with the LQI control in the middle or high frequency band. The suspension travel is very small in the middle or high frequency band, the suspension bottoming stop will not happen, so the vehicle ride quality can be improved apparently by the LQI control.

Decoupled nonsingular terminal sliding mode control for affine nonlinear systems

A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.

Linear systems toolkit in Matlab :structural decompositions and their applications

This paper presents a brief description of the software toolbox, linear systems toolkit, developed in Matlab environment. The toolkit contains 66 m-functious, including structural decompositions of linear autonomous systems, unforced/uuseused systems, proper systems, and singular systems, along with their applications to system factorizations, sensor/actuator selection, H-two and H-infinity control, and disturbance decoupling problems.

Adaptive trajectory linearization control for hypersonic reentry vehicle

This paper presents an improved design for the hypersonic reentry vehicle(HRV) by the trajectory linearization control(TLC) technology for the design of HRV. The physics-based model fails to take into account the external disturbance in the flight envelope in which the stability and control derivatives prove to be nonlinear and time-varying, which is likely in turn to increase the difficulty in keeping the stability of the attitude control system. Therefore, it is of great significance to modulate the unsteady and nonlinear characteristic features of the system parameters so as to overcome the disadvantages of the conventional TLC technology that can only be valid and efficient in the cases when there may exist any minor uncertainties. It is just for this kind of necessity that we have developed a fuzzy-neural disturbance observer(FNDO) based on the B-spline to estimate such uncertainties and disturbances concerned by establishing a new dynamic system. The simulation results gained by using the aforementioned technology and the observer show that it is just due to the innovation of the adaptive trajectory linearization control(ATLC) system. Significant improvement has been realized in the performance and the robustness of the system in addition to its fault tolerance.

Controllability and Observability of 2-DOF Permanent Magnet Maglev System with Linear Control

A new type of 2-DOF(degree of freedom) magnetic levitation system for multi-DOF levitation is proposed. In this system, the force of permanent magnets are used for levitation and controlled by adjusting the reluctance of the magnetic circuit. Using permanent magnets, the feature of this system is effective for saving energy and avoiding heat generation. First, the principle of the levitation system and typical reluctance control methods are described. Second, an experimental device based on the principle is introduced. Finally, the feasibility of this system is considered from linear control theory.

Design of bounded feedback controls for linear dynamical systems by using common Lyapunov functions

For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations.