Time-to-go weighted optimal trajectory shaping guidance law

For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.

Nonlinear Bayesian Estimation： From Kalman Filtering to a Broader Horizon

This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date,one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective,which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics(e.g., mean and covariance) conditioned on a system's measurement data.This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering(KF)techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.

Sliding mode control and Lyapunov based guidance law with impact time constraints

This paper analyses the issue of impact time control of super-cavitation weapons impact fixed targets which mainly refer to the ships or submarines who lost power, but still have combat capability. Control over impact time constraints of guidance law(ITCG) is derived by using sliding mode control(SMC) and Lyapunov stability theorem. The expected impact time is realized by using the notion of attack process and estimated time-to-go to design sliding mode surface(SMS). ITCG contains equivalent and discontinuous guidance laws, once state variables arrive at SMS,the equivalent guidance law keeps the state variables on SMS,then the discontinuous guidance law enforces state variables to move and reach SMS. The singularity problem of ITCG is also analyzed. Theoretical analysis and numerical simulation results are given to test the effectiveness of ITCG designed in this paper.

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

Homing Guidance Law with Falling Angle and Flying Time Control

In this paper,a new homing guidance method is used to control the flying time and falling angle for guided missiles. Through this approach,it finds the approximate solution to the quadratic equation of time-togo,which is used for the formula derivation of the flying time control command. In this guidance law design,the acceleration rate control command is adopted. The guidance law is composed of a PN guidance command and a flying time control command. Firstly,it obtains a desired falling angle with accurate guidance. Secondly,it introduces to satisfy the constraint of flying time. The flying time control requires an assumption on the future evolution of missile,which is called time-to-go. To cope with the time-varying speed of missiles,a method of compensating the estimation of time-to-go is presented. The new guidance law is evaluated by using a simulation of typical terminal guidance for rocket-propelled torpedo. The simulation results show that the guidance achieves excellent control performance and exhibits insensitivity to initial trajectory parameter over a widen flight envelope.

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

We first give a stabilized improved moving least squares （IMLS） approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.

Approximate Solutions to the Discontinuous Riemann-Hilbert Problem of Elliptic Systems of First Order Complex Equations

Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this article, we discuss approximate solutions to discontinuous Riemann-Hilbert boundary value problems, which have various applications in mechanics and physics. We first formulate the discontinuous Riemann-Hilbert problem for elliptic systems of first order complex equations in multiply connected domains and its modified well-posedness, then use the parameter extensional method to find approximate solutions to the modified boundary value problem for elliptic complex systems of first order equations, and then provide the error estimate of approximate solutions for the discontinuous boundary value problem.

A NEW ESPRIT METHOD FOR BLIND ESTIMATES OF DOA-DOPPLER FREQUENCY WITH UNKNOWN ARRAY MANIFOLD

A novel rotational invariance technique for blind estimates of direction of arrival (I)OA) and Doppler frequency with unknown array manifold due to array sensor uncertainties is proposed, taking Doppler frequency difference between a successive pulses as rotational parameter. The effectiveness of the new method is confirmed by computer simulation. Compared with the existing 2-D DOA-frequeucy estimate techniques, the computation load of the proposed method can be saved greatly.

A hybrid proportional navigation based two-stage impact time control guidance law

To improve applicability and adaptability of the impact time control guidance(ITCG) in practical engineering, a twostage ITCG law with simple but effective structure is proposed based on the hybrid proportional navigation, namely, the pureproportional-navigation and the retro-proportional-navigation.For the case with the impact time error less than zero, the first stage of the guided trajectory is driven by the retro-proportionalnavigation and the second one is driven by the pure-proportionalnavigation. When the impact time error is greater than zero, both of the stages are generated by the pure-proportional-navigation but using different navigation gains. It is demonstrated by twoand three-dimensional numerical simulations that the proposed guidance law at least has comparable results to existing proportional-navigation-based ITCG laws and is shown to be advantageous in certain circumstances in that the proposed guidance law alleviates its dependence on the time-to-go estimation, consumes less control energy, and adapts itself to more boundary conditions and constraints. The results of this research are expected to be supplementary to the current research literature.

Maximum Norm Estimates for Finite Volume Element Method for Non-selfadjoint and Indefinite Elliptic Problems

In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.

Extended trajectory shaping guidance law considering a first-order autopilot lag

To satisfy the terminal position and impact angel constraints,an optimal guidance problem was discussed for homing missiles. For a stationary or a slowly moving target on the ground,an extended trajectory shaping guidance lawconsidering a first-order autopilot lag（ ETSG L-C FAL） was proposed. To derive the ETSG L-C FAL,a time-to-go- nth power weighted objection function was adopted and three different derivation methods were demonstrated while the Schwartz inequality method was mainly demonstrated.The performance of the ETSG L-C FAL and the ETSG L guidance laws was compared through simulation.Simulation results showthat although a first-order autopilot is introduced into the ETSG L-C FAL guidance system,the position miss distance and terminal impact angle error induced by the impact angle is zero for different guidance time.

Critical Review on Improved Electrochemical Impedance Spectroscopy-cuckoo Search-Elman Neural Network Modeling Methods for Whole-life-cycle Health State Estimation of Lithium-ion Battery Energy Storage Systems

Efficient and accurate health state estimation is crucial for lithium-ion battery(LIB)performance monitoring and economic evaluation.Effectively estimating the health state of LIBs online is the key but is also the most difficult task for energy storage systems.With high adaptability and applicability advantages,battery health state estimation based on data-driven techniques has attracted extensive attention from researchers around the world.Artificial neural network(ANN)-based methods are often used for state estimations of LIBs.As one of the ANN methods,the Elman neural network(ENN)model has been improved to estimate the battery state more efficiently and accurately.In this paper,an improved ENN estimation method based on electrochemical impedance spectroscopy(EIS)and cuckoo search(CS)is established as the EIS-CS-ENN model to estimate the health state of LIBs.Also,the paper conducts a critical review of various ANN models against the EIS-CS-ENN model.This demonstrates that the EIS-CS-ENN model outperforms other models.The review also proves that,under the same conditions,selecting appropriate health indicators(HIs)according to the mathematical modeling ability and state requirements are the keys in estimating the health state efficiently.In the calculation process,several evaluation indicators are adopted to analyze and compare the modeling accuracy with other existing methods.Through the analysis of the evaluation results and the selection of HIs,conclusions and suggestions are put forward.Also,the robustness of the EIS-CS-ENN model for the health state estimation of LIBs is verified.

Efficient and accurate online estimation algorithm for zero-effort-miss and time-to-go based on data driven method

This paper introduces a novel and efficient algorithm for online estimation of zero-effortmiss and time-to-go based on data driven method.Only missile-target separations are utilized to construct the estimation models,and a practical Fisher fusion algorithm is derived to acquire the estimates with high accuracy and computational efficiency.Further,the two parameters can be online estimated at a particular time.Meanwhile,the kinematics equations of the missile-target engagement are independent,and assumptions of the missile guidance system dynamics and behaviors of the missile and target are completely out of consideration.Moreover,the effectiveness and applicability are explicitly verified through various simulation scenarios.

Local and global behavior for algorithms of solving equations

The theory of 'point estimate' and the concept of 'general convergence', which were put forward by Smale in order to investigate the complexity of algorithms for solving equations, have been producing a deep impact on the research about the local behavior, the semi-local behavior and the global behavior of iteration methods. The criterion of point estimate introduced by him not only provides a tool for quantitative analysis of the local behavior but also motivates the establishing of the unified determination for the semi-local behavior. Studying the global behavior in the view of discrete dynamical system will lead to many profound research subjects and open up a rich and colorful prospect. In this review, we will make a summarization about the research progress and some applications in nonsmooth optimizations.

Satellite proximate interception vector guidance based on differential games

This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire（CW） equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exoatmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations.

Remaining useful life estimation for deteriorating systems with time-varying operational conditions and condition-specific failure zones

Dynamic time-varying operational conditions pose great challenge to the estimation of system remaining useful life （RUL） for the deteriorating systems. This paper presents a method based on probabilistic and stochastic approaches to estimate system RUL for periodically moni- tored degradation processes with dynamic time-varying operational conditions and condition- specific failure zones. The method assumes that the degradation rate is influenced by specific oper- ational condition and moreover, the transition between different operational conditions plays the most important role in affecting the degradation process. These operational conditioqs are assumed to evolve as a discrete-time Markov chain （DTMC）. The failure thresholds are also determined by specific operational conditions and described as different failure zones. The 2008 PHM Conference Challenge Data is utilized to illustrate our method, which contains mass sensory signals related to the degradation process of a commercial turbofan engine. The RUE estimation method using the sensor measurements of a single sensor was first developed, and then multiple vital sensors were selected through a particular optimization procedure in order to increase the prediction accuracy. The effectiveness and advantages of the proposed method are presented in a comparison with exist- ing methods for the same dataset.

GLOBAL SOLUTION AND ITS LONG TIME BEHAVIOR FOR THE GENERALIZED LONG-SHORT WAVE EQUATIONS

The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a uniform a priori estimate for time. And also the dimensions of the global attractor are estimated.

Identification of the nonlinear properties of rubber-bearings in base-isolated buildings with limited seismic response data

Seismic behaviors of base-isolated structures are highly affected by the nonlinear characteristics of the isolated systems. Most of the currently available methods for the identification of nonlinear properties of isolator require either the measurements of all structural responses or the assumptions of the proper mathematic models for the rubber-bearings. In this paper, two algorithms are proposed to identify the nonlinear properties of rubber-bearings in base-isolated buildings using only partial measurements of structural dynamic responses. The first algorithm is applicable to the case that proper mathematical models are available for the base isolators. It is based on the extended Kalman filter for the parametric identification of nonlinear models of rubber-bearing isolators and buildings. For the general case where it is difficult to establish a proper mathematical model to describe the nonlinear behavior of a rubber-bearing isolator, another algorithm is proposed to identify the model-tYee nonlinear property of rubber-bearing isolated system. Nonlinear effect of rubber-bearing is treated as ＇fictitious loading＇ on the linear building under severe earthquake. The algorithm is based on the sequential Kalman estimator for the structural responses and the least-squares estimation of the ＇fictitious loading＇ to identify the nonlinear force of rubber-bearing isolator. Simulation results demonstrate that the proposed two algorithms are capable of identifying the nonlinear properties of rubber-bearing isolated systems with good accuracy.

MIXED FINITE ELEMENT METHODS FOR FRACTIONAL.NAVIER-STOKES EQUATIONS

This paper gives the detailed numerical analysis of mixed finite element method for fractional Navier-Stokes equations.The proposed method is based on the mixed finite element method in space and a finite difference scheme in time.The stability analyses of semi-discretization scheme and fully discrete scheme are discussed in detail.Furthermore,We give the convergence analysis for both semidiscrete and flly discrete schemes and then prove that the numerical solution converges the exact one with order O(h2+k),where h and k:respectively denote the space step size and the time step size.Finally,numerical examples are presented to demonstrate the effectiveness of our numerical methods.

ERROR ESTIMATES OF FINITE ELEMENT METHODS FOR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS

This paper studies the Galerkin finite element approximations of a class of stochas- tic fractionM differential equations. The discretization in space is done by a standard continuous finite element method and almost optimal order error estimates are obtained. The discretization in time is achieved via the piecewise constant, discontinuous Galerkin method and a Laplace transform convolution quadrature. We give strong convergence error estimates for both semidiscrete and fully discrete schemes. The proof is based on the error estimates for the corresponding deterministic problem. Finally, the numerical example is carried out to verify the theoretical results.