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.

Hybrid Synchronization of a Chen Hyper-Chaotic System with Two Simple Linear Feedback Controllers

This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability theory, and we verify our conclusion by numerical simulations.

Observer-Based Nonlinear Feedback Controls for Heartbeat ECG Tracking Systems

The analysis and design of observed-based nonlinear control of a heartbeat tracking system is investigated in this paper. Two of Zeeman’s heartbeat models are investigated and modified by adding the control input as a pacemaker, thereby creating the control-affine nonlinear system models that capture the general heartbeat behavior of the human heart. The control objective is to force the output of the heartbeat models to track and generate a synthetic electrocardiogram (ECG) signal based on the actual patient reference data, obtained from the William Beaumont Hospitals, Michigan, and the PhysioNet database. The formulations of the proposed heartbeat tracking control systems consist of two phases: analysis and synthesis. In the analysis phase, nonlinear controls based on input-output feedback linearization are considered. This approach simplifies the difficult task of developing nonlinear controls. In the synthesis phase, observer-based controls are employed, where the unmeasured state variables are estimated for practical implementations. These observer-based nonlinear feedback control schemes may be used as a control strategy in electronic pacemakers. In addition, they could be used in a software-based approach to generate a synthetic ECG signal to assess the effectiveness of diagnostic ECG signal processing devices.

Impact angle control over composite guidance law based on feedback linearization and finite time control

The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.

Sliding Mode Control Approach for Electrically Controllable Clutch of AMT Based on the Feedback Linearization

A sliding mode control approach based on the feedback linearization is proposed for the electrically controllable clutch of AMT vehicles. The nonlinear dynamic model for the hydraulic actuator associated with clutch is established. By means of the exact feedback linearization procedure of differential geometry, an equivalent, fully controllable and linear model is derived via a homomorphic transformation for the AMT clutch system.Furthermore, a sliding mode control is introduced to improve robustness. The tracking tests are performed using the sliding mode control on a Santana LX passenger car, and the experimental results prove that this nonlinear controller is of fine robustness and high degree of tracking accuracy.

Controlling Chaotic Behavior in a Bose-Einstein Condensate with Linear Feedback

The spatial structure of a Bose-Einstein condensate (BEC) loaded into an optical lattice potential isinvestigated and the spatially chaotic distributions of the condensates are revealed.A method of chaos control withlinear feedback is presented in this paper.By using the method,we propose a scheme of controlling chaotic behaviorin a BEG with atomic mirrors.The results of the computer simulation show that controlling the chaos into the stablestates could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the systemis negative.

CONTROLLING CHAOTIC OSCILLATIONS OF VISCO-ELASTIC PLATESBY THE LINEARIZATION VIA OUTPUTFEEDBACK

Controlling chaotic oscillations of viscoelastic plates are investigated in this paper. Based on the exact linearization method in nonlinear system control theory, a nonlinear feedback control law is presented for a class of non_affine control systems. The mathematical model describing motion of nonlinear viscoelastic plates is established, and it is simplified by the Galerkin method. The phase space portrait and the power spectrum are employed to demonstrate chaos in the system. The deflection is treated as an output, and is controlled to given periodic goals.

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.

Investigation on full vehicle height control algorithm using feedback linearization method

Aiming to improve the control accuracy of the vehicle height for the air suspension system,deeply analyzing the processes of variable mass gas thermodynamics and vehicle dynamics,a nonlinear height control model of the air suspension vehicle was built. To deal with the nonlinear characteristic existing in the lifting and lowering processes,the nonlinear model of vehicle height control was linearized by using a feedback linearization method. Then,based on the linear full vehicle model,the sliding model controller was designed to achieve the control variables. Finally,the nonlinear control algorithm in the original coordinates can be achieved by the inverse transformation of coordinates. To validate the accuracy and effectiveness of the sliding mode controller,the height control processes were simulated in Matlab,i. e.,the lifting and lowering processes of the air suspension vehicle were taken when vehicle was in stationary and driving at a constant speed. The simulation results show that,compared to other controllers,the designed sliding model controller based on the feedback linearization can effectively solve the ＂overshoot＂problem,existing in the height control process,and force the vehicle height to reach the desired value,so as to greatly improve the speed and accuracy of the height control process. Besides,the sliding mode controller can well regulate the roll and pitch motions of the vehicle body,thereby improving the vehicle＇s ride comfort.

Static output feedback control for discrete-time fuzzy bilinear system

The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.

H_∞ Output Feedback Control of Linear Time-invariant Fractional-order Systems over Finite Frequency Range

This paper focuses on the H_∞ output feedback control problem of linear time-invariant fractional-order systems over finite frequency range. Based on the generalized KalmanYakubovic-Popov(KYP) Lemma and a key projection lemma, a necessary and sufficient condition is established to ensure the existence of the H_∞ output feedback controller over finite frequency range, a desirable property in control engineering practice. By using the matrix congruence transformation, the feedback control gain matrix is decoupled and further parameterized by a scalar matrix. Two iterative linear matrix inequality algorithms are developed to solve this problem. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

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.

Tracking control of chaotic dynamical systems with feedback linearization

A new method was proposed for tracking the desired output of chaotic dy- namical system using the feedback linearization and nonlinear extended statement ob- server method. The feedback linearization was used to convert the nonlinear chaotic system into linear system. The extended Luenberger-like statements observer was de- signed to reconstructing and observing the unmeasured statements when the tracking controller was designed. By this way, the chaotic system could be forced to track vari- able desired output, which could be a time variant function or an equilibrium points. Taken the Lorenz chaotic system as example, the simulation results show the validity of the conclusion and effectiveness of the algorithm.

Feedback Linearization Optimal Control Approach for Bilinear Systems in CSTR Chemical Reactor

This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.

Dynamic inverse control of feedback linearization in ballistic correction based on nose cone swinging

It is a complicated nonlinear controlling problem to conduct a two-dimensional trajectory correction of rockets.By establishing the aerodynamic correction force mathematical model of rockets on nose cone swinging,the linear control is realized by the dynamic inverse nonlinear controlling theory and the three-time-scale separation method.The control ability and the simulation results are also tested and verified.The results show that the output responses of system track the expected curve well and the error is controlled in a given margin.The maximum correction is about±314 m in the lengthwise direction and±1 212 m in the crosswise direction from the moment of 5 s to the drop-point time when the angle of fire is 55°.Thus,based on the dynamic inverse control of feedback linearization,the trajectory correction capability of nose cone swinging can satisfy the requirements of two-dimensional ballistic correction,and the validity and effectiveness of the method are proved.

Nonlinear Control of Bioprocess Using Feedback Linearization, Backstepping, and Luenberger Observers

This paper addresses the analysis, design, and application of observer-based nonlinear controls by combining feedback linearization (FBL) and backstepping (BS) techniques with Luenberger observers. Complete development of observer-based controls is presented for a bioprocess. Controllers using input-output feedback linearization and backstepping techniques are designed first, assuming that all states are available for feedback. Next, the construction of observer in the transformed domain is presented based on input-output feedback linearization. This approach is then extended to observer design based on backstepping approach using the error equation resulted from the backstepping design procedure. Simulation results demonstrating the effectiveness of the techniques developed are presented and compared.

General Integral Control Design via Feedback Linearization

Based on the feedback linearization technique, we present a systematic design method for the General Integral Control and a new integral control strategy along with a class of fire-new integrator. By using the linear system theory and Lyapunov method along with LaSalle’s invariance principle, the conditions on the control gains to ensure regionally as well as semi-globally asymptotic stability are provided. Theoretical analysis and simulation results demonstrated that: by using this design method, General Integral Control can deal with nonlinearity and uncertainties of dynamics more effectively;the optimum response can be achieved in the whole control domain, even under uncertain payload and varying-time disturbances. This means that General Integral Control has strong robustness, fast convergence, good flexibility, and then makes the engineers design a high performance controller more easily.

Feedforward and feedback optimal control for linear time-varying systems with persistent disturbances

The optimal control problem was studied for linear time-varying systems,which was affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions. To damp the effect of disturbances in an optimal fashion,we obtained a new feedforward and feedback optimal control law and gave the control algorithm by solving a Riccati differential equation and a matrix differential equation. Simulation results showed that the achieved optimal control law was realizable,efficient and robust to reject the external disturbances.