Pure State Feedback Switching Control Based on the Online Estimated State for Stochastic Open Quantum Systems

For the n-qubit stochastic open quantum systems,based on the Lyapunov stability theorem and LaSalle’s invariant set principle,a pure state switching control based on on-line estimated state feedback(short for OQST-SFC)is proposed to realize the state transition the pure state of the target state including eigenstate and superposition state.The proposed switching control consists of a constant control and a control law designed based on the Lyapunov method,in which the Lyapunov function is the state distance of the system.The constant control is used to drive the system state from an initial state to the convergence domain only containing the target state,and a Lyapunov-based control is used to make the state enter the convergence domain and then continue to converge to the target state.At the same time,the continuous weak measurement of quantum system and the quantum state tomography method based on the on-line alternating direction multiplier(QST-OADM)are used to obtain the system information and estimate the quantum state which is used as the input of the quantum system controller.Then,the pure state feedback switching control method based on the on-line estimated state feedback is realized in an n-qubit stochastic open quantum system.The complete derivation process of n-qubit QST-OADM algorithm is given;Through strict theoretical proof and analysis,the convergence conditions to ensure any initial state of the quantum system to converge the target pure state are given.The proposed control method is applied to a 2-qubit stochastic open quantum system for numerical simulation experiments.Four possible different position cases between the initial estimated state and that of the controlled system are studied and discussed,and the performances of the state transition under the corresponding cases are analyzed.

Comparative Study of Trajectory Tracking Control for Automated Vehicles via Model Predictive Control and Robust H-infinity State Feedback Control

A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC controllers’performance in tracking predefined trajectory under different scenarios.MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire,which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode.RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison.Then,three test cases are built in CarSim-Simulink joint platform.Specifically,the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions.Besides,the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability.Furthermore,an extreme curve test is built where the road adhesion changes suddenly,in order to test the performance of both controllers under extreme conditions.Finally,the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.

The feedback control of fractional order unified chaotic system

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

State Feedback Sliding Mode Control without Chattering by Constructing Hurwitz Matrix for AUV Movement

This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.

Mixed H_2/H_∞ State Feedback Attitude Control of Microsatellite Based on Extended LMI Method

For the appearance of the additive perturbation of controller gain when the controller parameter has minute adjustment at the initial running stage of system,to avoid the adverse effects,this paper investigates the mixed H_2/H_∞ state feedback attitude control problem of microsatellite based on extended LMI method.Firstly,the microsatellite attitude control system is established and transformed into corresponding state space form.Then,without the equivalence restriction of the two Lyapunov variables of H_2 and H∞performance,this paper introduces additional variables to design the mixed H_2/H_∞ control method based on LMI which can also reduce the conservatives.Finally,numerical simulations are analyzed to show that the proposed method can make the satellite stable within 20 s whether there is additive perturbation of the controller gain or not.The comparative analysis of the simulation results between extended LMI method and traditional LMI method also demonstrates the effectiveness and feasibility of the proposed method in this paper.

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.

Direct Yaw Moment Control for Distributed Drive Electric Vehicle Handling Performance Improvement

For a distributed drive electric vehicle（DDEV） driven by four in-wheel motors, advanced vehicle dynamic control methods can be realized easily because motors can be controlled independently, quickly and precisely. And direct yaw-moment control（DYC） has been widely studied and applied to vehicle stability control. Good vehicle handling performance： quick yaw rate transient response, small overshoot, high steady yaw rate gain, etc, is required by drivers under normal conditions, which is less concerned, however. Based on the hierarchical control methodology, a novel control system using direct yaw moment control for improving handling performance of a distributed drive electric vehicle especially under normal driving conditions has been proposed. The upper-loop control system consists of two parts： a state feedback controller, which aims to realize the ideal transient response of yaw rate, with a vehicle sideslip angle observer; and a steering wheel angle feedforward controller designed to achieve a desired yaw rate steady gain. Under the restriction of the effect of poles and zeros in the closed-loop transfer function on the system response and the capacity of in-wheel motors, the integrated time and absolute error（ITAE） function is utilized as the cost function in the optimal control to calculate the ideal eigen frequency and damper coefficient of the system and obtain optimal feedback matrix and feedforward matrix. Simulations and experiments with a DDEV under multiple maneuvers are carried out and show the effectiveness of the proposed method： yaw rate rising time is reduced, steady yaw rate gain is increased, vehicle steering characteristic is close to neutral steer and drivers burdens are also reduced. The control system improves vehicle handling performance under normal conditions in both transient and steady response. State feedback control instead of model following control is introduced in the control system so that the sense of control intervention to drivers is relieved.

H_∞ drift control of time-delayed seismic structures

In this paper, an optimal H∞ control algorithm was applied to the design of an active tendon system installed at the first story of a multi-story building to reduce its interstory drift due to earthquake excitations. To achieve optimal control performance and to guarantee the stability of the control system, an optimum strategy to select control parameters γ and α was developed. Analytical expressions of the upper and the lower bounds of γ and α were obtained for a single degree-of-freedom system with state feedback control. The selection ranges for both γ and α are graphically defined so that the controlled system is always stable and the control performance is better than by the conventional LQR control algorithm. Numerical results from a controlled three-story building under real earthquake excitations demonstrate that the peak first interstory drift can be significantly reduced with maximum control force around 10% of the building weight. An optimum design flow chart was provided. In addition, for a time-delayed structure, this study gave explicit formulae to calculate the critical values of γ and a. The system stability and control performance can thus be guaranteed even with time delay.

Delay-dependent H_(2)/H_(∞) Control for Vehicle Magneto-rheological Semi-active Suspension

The exist researches of the magneto-rheological semi-active suspension(MSAS) control mainly focus on the design of control laws,which aim at obtaining an optimal control strategy to improve the ride comfort and handling stability.In the controller design,the stability of the MSAS system cannot be confirmed owing to the control input time delay considered little.In this paper,a quarter vehicle MSAS model with time-delay is built.Therefore,through formulating the sprung mass acceleration suitably as the optimization object,suspension deflection and tyre dynamic load and coulomb damping force as the constraint objects,with considering the control input time-delay,a delay-dependent state feedback H2/H∞ controller is designed.According to Lyapunov-Krasovskii functional theory,the sufficient conditions for asymptotic stability and the existence of delay-dependent H2/H∞ controller are obtained,and the controller design is transformed into the minimization problem for linear function through linear matrix inequality(LMI).Random road excitation simulations and experiments are carried out.The simulation and experiment results show that the design can preserve the closed-loop stability and achieve the performances for MSAS system in spite of the existence of the control input time-delay.The present study can provide an important basis and method for research on time-delay problem in MSAS and other chassis subsystems.

Research on robust control strategy of single DOF supporting system of MLDSB based on H∞ mixed-sensitivity Method

Because of hydraulic-electromagnetic double supporting forms,the supporting capacity and stiffness of magnetic-liquid double suspension bearing(MLDSB)can be improved sharply and then it is more suitable for medium speed,heavy load and frequent-starting occasions.Due to the multiple uncertainty,such as the coupling,the unmodeled dynamics,the parameter perturbation and the external disturbance perturbation,the robust stability and stiffness of control system of MLDSB are hard to meet the design requirements.Firstly,the structural features and the regulation mechanisms of MLDSB are presented and the radial 4-DOF kinetic equations are established.Secondly,the influence factors of the control system's coupling on unbalanced vibration caused by the deviation of the rotor center of mass are revealed,and then the weighting function of suppressing the unbalanced vibration can be obtained.Finally,H∞ controller of MLDSB is designed with H∞ mixed-sensitivity method,and the control performances of H∞ controller is compared with the state feedback controller.The simulation results show that single degree of freedom(DOF)supporting system of MLDSB with H∞ controller has good robust stability,stiffness and the ability to suppress unbalanced external disturbances.This study can provide the theoretical reference for stabilized suspension and control of MLDSB.

Stabilizing controller design for nonlinear fractional order systems with time varying delays

To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the Mittag-Lefler function,Laplace transform and Gronwall inequality,a linear stabilizing controller is derived,which uses the fractional order of the delayed system and the upper bound of system nonlinear functions.In the second method,at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality(LMI)which can easily be solved.Then,on the basis of this result,a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds.Simulation results show the effectiveness of the proposed methods.

Singular Stabilization and H_∞ Control of Nonlinear Systems with Ordinary Homogeneous Properties

In this paper, the nonlinear singular stabilization, H∞ control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogeneous. Secondly, by vitue of Hamilton-Jacobi-Isaacs equations or inequalities, we solve regular H∞ of nonlinear systems with homogeneous properties. To overcome the H∞ problem of singular nonlinear system, we try to transform inputs of the singular nonlinear system into two parts： regular part input and singular part input. Following the previous results, we solve the singular nonlinear system H∞ control, we give the Lyapunov function and the state feedback controller of the singular nonlinear systems with homogeneous properties.

Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions

The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilization of uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robust stability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, showing the advanteges of the proposed method.

Adaptive stabilization for cascade nonlinear systems

An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF) techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

Impulsive state feedback control during the sulphitation reaction in process of manufacture of sugar

In this paper,the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacturo of sugar is considered.By means of square approximation and a series of switched systems,the periodic solution is approximated by a series of continuous hybrid limit cycles.Similar to the analysis of limit cycles of continuous systems,the existence and stability criteria of the order-1 periodic solution are obtained.Further,numerical analysis and discussion are given.

New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Descriptor Systems

The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.

Non-fragile memory feedback control for uncertain time-varying delay switched fuzzy systems with unknown nonlinear disturbance

Currently,the feedback control rate of most nonlinear systems is realised by the memoryless state feedback controller which cannot affect the impact of time delay on the systems,and the general processing method of the Lyapunov–Krasovskii functional for the time-varying delay switched fuzzy systems(SFS)is more conservative.Therefore,this paper addresses the problem of nonfragile robust and memory state feedback control for switched fuzzy systems with unknown nonlinear disturbance.Non-fragile memory state feedback robust controller which has two controller gains different from each other,and switching law are designed to keep the proposed systems asymptotically stable for all admissible parameter uncertainties.Delay-dependent less conservative sufficient conditions are obtained through using the Lyapunov–Krasovskii functional method and free-weighting matrices depending on Leibniz–Newton,guaranteeing that the SFS can be asymptotically stable.A numerical example is given to illustrate the proposed controller performs better than the classic memoryless state feedback controller.

Stability and Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model

The observed dynamical property illustrates that state feedback control may stabilize invariant attractor to stable state in a simple version of hematopoietic stem cell model. The stability character of the positive steady state is analyzed by the computation of the rightmost characteristic roots in complex plane. Hopf bifurcation points are tracked as the roots curve crossing imaginary axis from the left half plane to the right half plane continuously. The bifurcation direction and stability of the bifurcating periodical solution are discussed by norm form computation combined with the center manifold theory. Furthermore, the numerical simulation verifies that instead of chaos, system is stabilized to period-1, 2, 3, 4 and period-7 periodical solutions in some delay windows, and the continuous of periodical solutions is also numerical simulated with varying free parameters continuously.

Approximate Synchronization of Multi-Agent Systems over Finite Fields

In this paper,the approximate synchronization of leader-follower multiagent systems(MASs) over finite fields is studied in regard to local and global synchronization.First,the approximately synchronous state set(ASSS) is obtained.Second,combined with ASSS and transient periods,some criteria for the local and global approximate synchronization of systems are given.Moreover,the algorithms for calculating the maximum approximately synchronous basin(MASB) and the maximum control invariant set(MCIS) are presented.Third,the global approximate synchronization of the system is achieved by designing the state feedback control,and a design algorithm of the controller using the truth matrix method is proposed.Moreover,the results of approximate synchronization are degenerated to complete synchronization.Last,two examples are shown to demonstrate the results of this paper.