Robust controller design for compound control missile with fixed bounded convergence time

A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer(ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller.

Differential geometric guidance command with finite time convergence using extended state observer

For improving the performance of differential geometric guidance command(DGGC), a new formation of this guidance law is proposed, which can guarantee the finite time convergence(FTC) of the line of sight(LOS) rate to zero or its neighborhood against maneuvering targets in three-dimensional(3D) space. The extended state observer(ESO) is employed to estimate the target acceleration, which makes the new DGGC more applicable to practical interception scenarios. Finally, the effectiveness of this newly proposed guidance command is demonstrated by the numerical simulation results.

Long-time Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅱ)

In this article we extend ours framework of long time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1—28”, to the Gauss Ledendre full discretization. When apply the result to the Crank Nicholson finiteelement full discretization of the Navier Stokes equations, we can remore the grid ratio restriction of “Heywood, J. G. and Rannacher, R., SIAM J. Numer. Anal., 27(1990), 353—384”, and weaken the stability condition on the continuous solution.

Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization

We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d（Ah,τ, .A） → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.

Cooperative guidance law based on super-twisting observer for target maneuvering

To solve the problem that multiple missiles should simultaneously attack unmeasurable maneuvering targets,a guidance law with temporal consistency constraint based on the super-twisting observer is proposed.Firstly,the relative motion equations between multiple missiles and targets are established,and the topological model among multiple agents is considered.Secondly,based on the temporal consistency constraint,a cooperative guidance law for simultaneous arrival with finite-time convergence is derived.Finally,the unknown target maneuver-ing is regarded as bounded interference.Based on the second-order sliding mode theory,a super-twisting sliding mode observer is devised to observe and track the bounded interfer-ence,and the stability of the observer is proved.Compared with the existing research,this approach only needs to obtain the sliding mode variable which simplifies the design process.The simulation results show that the designed cooperative guidance law for maneuvering targets achieves the expected effect.It ensures successful cooperative attacks,even when confronted with strong maneuvering targets.

Convergence Analysis of Cuckoo Search by Creating Markov Chain

Cuckoo search(CS) has been used successfully for solving global optimization problems.From a theoretical point of view,the convergence of the CS is an important issue.In this paper,convergence analysis of CS was studied.The transition probability characteristics of the population to construct a Markov chain were analyzed.The homogeneity of the Markov chain was derived based on stochastic process theory.Then it was proved to be an absorbing state Markov chain.Consequently,the global convergence of CS was deduced based on conditions of convergence sequence and total probability formula,and the expected convergence time was given.Finally,a series of experiments were conducted.Experimental results were analyzed and it is observed that CS seems to perform better than PSO.

Convergence Curve for Non-Blind Adaptive Equalizers

In this paper a closed-form approximated expression is proposed for the Intersymbol Interference (ISI) as a function of time valid during the entire stages of the non-blind adaptive deconvolution process and is suitable for the noisy, real and two independent quadrature carrier input case. The obtained expression is applicable for type of channels where the resulting ISI as a function of time can be described with an exponential model having a single time constant. Based on this new expression for the ISI as a function of time, the convergence time (or number of iteration number required for convergence) of the non-blind adaptive equalizer can be calculated. Up to now, the equalizer’s performance (convergence time and ISI as a function of time) could be obtained only via simulation when the channel coefficients were known. The new proposed expression for the ISI as a function of time is based on the knowledge of the initial ISI and channel power (which is measurable) and eliminates the need to carry out any more the above mentioned simulation. Simulation results indicate a high correlation between the simulated and calculated ISI (based on our proposed expression for the ISI as a function of time) during the whole deconvolution process for the high as well as for the low signal to noise ratio (SNR) condition.

TIME ASYMPTOTIC BEHAVIOR OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate （1 ＋ t）^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate （1 ＋ t）^-1/4 which is slower than the rate （1 ＋ t）^-3/4 for the compressible Navier-Stokes equations （NS）. In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate （1 ＋ t）^-3/4＋ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

The isentropic bipolar compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l（R3） ∩ B˙ s 1,1 （R3） with l ≥ 4 and s ∈ （0, 1], it is shown that the momenta of the charged particles decay at the optimal rate （1＋t） 1 4 s 2 in L2 -norm, which is slower than the rate （1＋t） 3 4 s 2 for the compressible Navier-Stokes （NS） equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both （1 ＋ t） 3 4 due to the cancellation effect from the interplay interaction of the charged particles.

Timing of the Early Paleozoic Yangtze and Cathysian Convergence： Constraint from U-Pb Geochronology of Hydrothermal Zircons from Mafic Mylonite within the Shoucheng-Piaoli Ductile Shear Zone, Northern Guangxi

Objective The northern Guangxi region is in the southwestern part of the Southern China continent,which is located at the junction of the southwest section of the Early Paleozoic Yangtze block and Cathaysian block.A series of NNE-trending ductile shear zones are developed in this region,and these ductile shear zones are mostly previously suggested boundary faults of the Early Paleozoic Yangtze block and Cathaysian block,such as the Shoucheng–Piaoli ductile shear zone in Northern Guangxi （Meng Yuanku et al., 2016; Zhang Xuefeng et al., 2015）.

Trajectory tracking and obstacle avoidance method for robots based on fast terminal sliding mode

For accurate trajectory tracking and obstacle avoidance in finite time of a nonholonomic mobile robot,a trajectory tracking controller based on global fast terminal sliding mode method is proposed,which has the advantages of chattering-free and adjustable convergence time.First of all,the kinematics model of the robot is established in mobile carrier coordinates.Secondly,the global structure including terminal attractor and exponential convergence of the fast terminal sliding mode trajectory tracking controller is proved by Lyapunov stability theory,ensuring that the trajectory and heading angle tracking error converges to a smaller zero range in finite time.Finally,the artificial potential field obstacle avoidance method is introduced to make the robot not only track the reference trajectory strictly,but also avoid the obstacles.The simulation results show that the proposed method can achieve a stable tracking control in finite time for a given reference trajectory.

Adaptive terminal sliding mode control for high-order nonlinear dynamic systems

An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

Nonlinear robust control of a quadrotor helicopter with finite time convergence

In this paper, the control problem for a quadrotor helicopter which is subjected to modeling uncertainties and unknown external disturbance is investigated. A new nonlinear robust control strategy is proposed. First, a nonlinear complementary filter is developed to fuse the raw data from the onboard barometer and the accelerometer to decrease the negative effects from the noise associated with the low-cost onboard sensors Then the adaptive super-twisting methodology is combined with a backstepping method to formulate the nonlinear robust controller for the quadrotor＇s attitude angles and the altitude position. Lyapunov based stability analysis shows that finite time convergence is ensured for the closed-loop operation of the quadrotor＇s roll angle, pitch angle, row angle and the altitude position. Real-time flight experimental results, which are performed on a quadrotor flight testbed, are included to demonstrate the good control performance of the proposed control methodology.

Controlling Chaos in Hénon Map by the Constant Feedback Method

We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise.

THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATIONS

In this paper we use the spectral method to analyse the generalized Kuramoto-Sivashinsky equations. We prove the existence and uniqueness of global smooth solution of the equations. Finally, we obtain the error estimation between spectral approximate solution and exact solution on large time.

THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ)

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors AN, ANk respectively and d(AN, A) → 0, d(ANk, A) → 0.

Perfect synchronization of chaotic systems： a controllability perspective

This paper presents a synchronization method, motivated from the constructive controllability analysis, for two identical chaotic systems. This technique is applied to achieve perfect synchronization for Lorenz systems and coupled dynamo systems. It turns out that states of the drive system and the response system are synchronized within finite time, and the reaching time is independent of initial conditions, which can be specified in advance. In addition to the simultaneous synchronization, the response system is synchronized un-simultaneously to the drive system with different reaching time for each state. The performance of the resulting system is analytically quantified in the face of initial condition error, and with numerical experiments the proposed method is demonstrated to perform well.

Comprehensive assessment of real-time precise products from IGS analysis centers

Real-Time Precise Point Positioning(RT-PPP)has been one of the research hotspots in GNSS(Global Navigation Satellite System)community for decades.Real-time precise products of satellite orbits and clocks are the prerequisite for RT-PPP.Thus,it is of great importance to investigate the current multi-GNSS real-time precise products in State Space Representation(SSR)from diferent analysis centers.In this article,SSR products from 10 analysis centers are comprehensively evaluated by comparing them with the fnal products and performing the kinematic PPP.The results show that analysis centers CNES(Centre National D’Etudes Spatiales)and WHU(GNSS Research Center of Wuhan University)provide the most complete products with the best quality.Concerning the accuracy of real-time products for the GNSSs,the accuracies of orbit and clock products are better than 5 cm and 0.15 ns,respectively,for Global Positioning System(GPS),followed by Galileo navigation satellite system(Galileo),BeiDou-3 Navigation Satellite System(BDS-3),GLObal NAvigation Satellite System(GLONASS),and BeiDou-2 Navigation Satellite System(BDS-2).Meanwhile,the results of the RT-PPP with quad-system show that the positioning accuracies are 1.76,1.12 and 2.68 cm in east,north,and up directions,respectively,and the convergence time to 0.1,0.1,0.2 m for corresponding directions is 15.35 min.

Robust Chattering-Free Finite Time Attitude Tracking Control with Input Saturation

This paper addresses the attitude tracking control problem of a rigid spacecraft in the presence of the modeling uncertainty,external disturbance,and saturated control input by designing two robust att计ude tracking controllers.The basic controller is formulated using an integral sliding mode surface which is continuous and provides an asymptotic convergence rate for the closed-loop system.In this case,only the external disturbance with the prior information is considered.Then,to provide a finite time convergence rate and further improve the robustness of the control system under the unknown system uncertainty containing both the modeling uncertainty and external disturbance,a novel integral terminal sliding mode surface(ITSMS)is designed and associated w计h the continuous adaptive control method.Besides,a command filter is utilized to deal with the immeasurability problem within the proposed ITSMS and an auxiliary system to counteract the input saturation problem.Digital simulations are presented to verify the effectiveness of the proposed controllers.