Mathematical Problems in Engineering The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Discrete Multiwavelet Critical-Sampling Transform-Based OFDM System over Rayleigh Fading Channels Sun, 24 May 2015 12:01:40 +0000 Discrete multiwavelet critical-sampling transform (DMWCST) has been proposed instead of fast Fourier transform (FFT) in the realization of the orthogonal frequency division multiplexing (OFDM) system. The proposed structure further reduces the level of interference and improves the bandwidth efficiency through the elimination of the cyclic prefix due to the good orthogonality and time-frequency localization properties of the multiwavelet transform. The proposed system was simulated using MATLAB to allow various parameters of the system to be varied and tested. The performance of DMWCST-based OFDM (DMWCST-OFDM) was compared with that of the discrete wavelet transform-based OFDM (DWT-OFDM) and the traditional FFT-based OFDM (FFT-OFDM) over flat fading and frequency-selective fading channels. Results obtained indicate that the performance of the proposed DMWCST-OFDM system achieves significant improvement compared to those of DWT-OFDM and FFT-OFDM systems. DMWCST improves the performance of the OFDM system by a factor of 1.5–2.5 dB and 13–15.5 dB compared with the DWT and FFT, respectively. Therefore the proposed system offers higher data rate in wireless mobile communications. Sameer A. Dawood, F. Malek, M. S. Anuar, and Suha Q. Hadi Copyright © 2015 Sameer A. Dawood et al. All rights reserved. Advances in Finite Element Method 2014 Sun, 24 May 2015 11:53:55 +0000 Song Cen, Chenfeng Li, Sellakkutti Rajendran, and Zhiqiang Hu Copyright © 2015 Song Cen et al. All rights reserved. Finite-Time Consensus Algorithm for Multiple Nonholonomic Disturbed Systems with Its Application Sun, 24 May 2015 11:35:12 +0000 This paper deals with the problem of finite-time consensus of multiple nonholonomic disturbed systems. To accomplish this problem, the multiple nonholonomic systems are transformed into two multiple subsystems, and these two multiple subsystems are studied, respectively. For these two multiple subsystems, the terminal sliding mode (TSM) algorithms are designed, respectively, which achieve the finite-time reaching of sliding surface. Next, a switching control strategy is proposed to guarantee the finite-time consensus of all the states for multiple nonholonomic systems with disturbances. Finally, we demonstrate the effectiveness of the proposed consensus algorithms with application to multiple nonholonomic mobile robots. Shang Shi, Xin Yu, and Guohai Liu Copyright © 2015 Shang Shi et al. All rights reserved. Block-Matching Based Multifocus Image Fusion Sun, 24 May 2015 11:32:12 +0000 A new multifocus image fusion method is proposed. Two image blocks are selected by sliding the window from the two source images at the same position, discrete cosine transform (DCT) is implemented, respectively, on these two blocks, and the alternating component (AC) energy of these blocks is then calculated to decide which is the well-focused one. In addition, block matching is used to determine a group of image blocks that are all similar to the well-focused reference block. Finally, all the blocks are returned to their original positions through weighted average. The weight is decided with the AC energy of the well-focused block. Experimental results demonstrate that, unlike other spatial methods, the proposed method effectively avoids block artifacts. The proposed method also significantly improves the objective evaluation results, which are obtained by some transform domain methods. Feng Zhu, Yingkun Hou, and Jingyu Yang Copyright © 2015 Feng Zhu et al. All rights reserved. Smoothing Algorithm for Planar and Surface Mesh Based on Element Geometric Deformation Sun, 24 May 2015 06:42:07 +0000 Smoothing is one of the basic procedures for improvement of mesh quality. In this paper, a novel and efficient smoothing approach for planar and surface mesh based on element geometric deformation is developed. The presented approach involves two main stages. The first stage is geometric deformation of all the individual elements through a specially designed two-step stretching-shrinking operation (SSO), which is performed by moving the vertices of each element according to a certain rule in order to get better shape of the element. The second stage is to determine the position of each node of the mesh by a weighted average strategy according to quality changes of its adjacent elements. The suggested SSO-based smoothing algorithm works efficiently for triangular mesh and can be naturally expanded to quadrilateral mesh, arbitrary polygonal mesh, and mixed mesh. Combined with quadratic error metric (QEM), this approach may be also applied to improve the quality of surface mesh. The proposed method is simple to program and inherently very suitable for parallelization, especially on graphic processing unit (GPU). Results of numerical experiments demonstrate the effectiveness and potential of this method. Shuli Sun, Minglei Zhang, and Zhihong Gou Copyright © 2015 Shuli Sun et al. All rights reserved. Nonlinear Coupling Characteristics Analysis of Integrated System of Electromagnetic Brake and Frictional Brake of Car Thu, 21 May 2015 15:11:22 +0000 Since theoretical guidance is lacking in the design and control of the integrated system of electromagnetic brake and frictional brake, this paper aims to solve this problem and explores the nonlinear coupling characteristics and dynamic characteristics of the integrated system of electromagnetic brake and frictional brake. This paper uses the power bond graph method to establish nonlinear coupling mathematical model of the integrated system of electromagnetic brake and frictional brake and conducts the contrastive analysis on the dynamic characteristics based on this mathematical model. Meanwhile, the accuracy of the nonlinear coupling mathematical model proposed above is verified on the hardware in the loop simulation platform, and nonlinear coupling characteristics of the integrated system are also analyzed through experiments. Ren He and Donghai Hu Copyright © 2015 Ren He and Donghai Hu. All rights reserved. Periodic Wave Solutions and Their Limit Forms of the Modified Novikov Equation Thu, 21 May 2015 14:30:58 +0000 The modified Novikov equation is studied by using the bifurcation theory of dynamical system and the method of phase portraits analysis. The existences, dynamic properties, and limit forms of periodic wave solutions for being a negative even are investigated. All possible exact parametric representations of the different kinds of nonlinear waves also are presented. Qing Meng and Bin He Copyright © 2015 Qing Meng and Bin He. All rights reserved. An Improved Optimal Capacity Ratio Design Method for WSB/HPS System Based on Complementary Characteristics of Wind and Solar Thu, 21 May 2015 14:17:50 +0000 The reliability and economic value of wind and solar power generation system with energy storage are decided by the balance of capacity distribution. The improved capacity balance matching method is proposed in this paper, which not only utilizes the complementary characteristics of the wind and solar power generation system sufficiently but also reduces the charge and discharge times of the battery. Therefore, the generation reliability is improved and the working lifetime of the whole system is lengthened. Consequently, the investment of the battery energy storage is reduced as well as the whole cost is decreased. The experimental result was presented to verify the effectiveness of the improved optimal capacity ratio design method. Xiaoju Yin, Fengge Zhang, Zhenhe Ju, and Yonggang Jiao Copyright © 2015 Xiaoju Yin et al. All rights reserved. Nonlinear Stability Analysis of a Composite Girder Cable-Stayed Bridge with Three Pylons during Construction Thu, 21 May 2015 13:21:21 +0000 Based on the nonlinear stability analysis method, the 3D nonlinear finite element model of a composite girder cable-stayed bridge with three pylons is established to research the effect of factors including geometric nonlinearity, material nonlinearity, static wind load, and unbalanced construction load on the structural stability during construction. Besides, the structural nonlinear stability in different construction schemes and the determination of temporary pier position are also studied. The nonlinear stability safety factors are calculated to demonstrate the rationality and safety of construction schemes. The results show that the nonlinear stability safety factors of this bridge during construction meet the design requirement and the minimum value occurs in the maximum double cantilever stage. Besides, the nonlinear stability of the structure in the side of edge-pylon meets the design requirement in the two construction schemes. Furthermore, the temporary pier can improve the structure stability, effectively, and the actual position is reasonable. In addition, the local buckling of steel girder occurs earlier than overall instability under load in some cable tension stages. Finally, static wind load and the unbalanced construction load should be considered in the stability analysis for the adverse impact. Xiaoguang Deng and Muyu Liu Copyright © 2015 Xiaoguang Deng and Muyu Liu. All rights reserved. Adaptive Output Tracking Control for Nonlinear Systems with Failed Actuators and Aircraft Flight System Applications Thu, 21 May 2015 12:59:39 +0000 An adaptive failure compensation scheme using output feedback is proposed for a class of nonlinear systems with nonlinearities depending on the unmeasured states of systems. Adaptive high-gain K-filters are presented to suppress the nonlinearities while the proposed backstepping adaptive high-gain controller guarantees the stability of the closed-loop system and small tracking errors. Simulation results verify that the adaptive failure compensation scheme is effective. Chuanjing Hou, Lisheng Hu, and Yingwei Zhang Copyright © 2015 Chuanjing Hou et al. All rights reserved. Second-Order Super-Twisting Sliding Mode Control for Finite-Time Leader-Follower Consensus with Uncertain Nonlinear Multiagent Systems Thu, 21 May 2015 12:57:24 +0000 Consensus tracking problem of the leader-follower multiagent systems is resolved via second-order super-twisting sliding mode control approach. The followers’ states can keep consistent with the leader’s states on sliding surfaces. The proposed approach can ensure the finite-time consensus if the directed graph of the nonlinear system has a directed path under the condition that leader’s control input is unavailable to any followers. It is proved by using the finite-time Lyapunov stability theory. Simulation results verify availability of the proposed approach. Nan Liu, Rui Ling, Qin Huang, and Zheren Zhu Copyright © 2015 Nan Liu et al. All rights reserved. Study on Real-Time Simulation Analysis and Inverse Analysis System for Temperature and Stress of Concrete Dam Thu, 21 May 2015 12:43:02 +0000 In the concrete dam construction, it is very necessary to strengthen the real-time monitoring and scientific management of concrete temperature control. This paper constructs the analysis and inverse analysis system of temperature stress simulation, which is based on various useful data collected in real time in the process of concrete construction. The system can produce automatically data file of temperature and stress calculation and then achieve the remote real-time simulation calculation of temperature stress by using high performance computing techniques, so the inverse analysis can be carried out based on a basis of monitoring data in the database; it fulfills the automatic feedback calculation according to the error requirement and generates the corresponding curve and chart after the automatic processing and analysis of corresponding results. The system realizes the automation and intellectualization of complex data analysis and preparation work in simulation process and complex data adjustment in the inverse analysis process, which can facilitate the real-time tracking simulation and feedback analysis of concrete temperature stress in construction process and enable you to discover problems timely, take measures timely, and adjust construction scheme and can well instruct you how to ensure project quality. Lei Zhang, Yi Liu, Bingqi Li, Guoxin Zhang, and Songtao Zhang Copyright © 2015 Lei Zhang et al. All rights reserved. Synchronization of Lorenz System Based on Fast Stabilization Sliding Mode Control Thu, 21 May 2015 12:07:47 +0000 A sliding mode control approach is achieved for Lorenz system based on optimal finite time convergent and integral sliding mode surface. The system perturbation is divided into two parts: the unmatched and the matched parts. Firstly, we design a discontinuous control for the unmatched part which will not be amplified. Secondly, we design a continuous control, that is, the ideal control to stabilize the Lorenz system error states in finite time stabilization. Then the controller based on integral sliding mode is constructed to ensure the robustness. The proposed method is proven to guarantee the stability and the robustness using the Lyapunov theory in the system uncertainties and external perturbation. Finally, the numerical simulations demonstrate that the proposed controller is effective and robust with respect to the perturbation. Xu Guowei, Wan Zhenkai, and Li Chunqing Copyright © 2015 Xu Guowei et al. All rights reserved. Design Method of Active Disturbance Rejection Variable Structure Control System Thu, 21 May 2015 09:44:34 +0000 Based on lines cluster approaching theory and inspired by the traditional exponent reaching law method, a new control method, lines cluster approaching mode control (LCAMC) method, is designed to improve the parameter simplicity and structure optimization of the control system. The design guidelines and mathematical proofs are also given. To further improve the tracking performance and the inhibition of the white noise, connect the active disturbance rejection control (ADRC) method with the LCAMC method and create the extended state observer based lines cluster approaching mode control (ESO-LCAMC) method. Taking traditional servo control system as example, two control schemes are constructed and two kinds of comparison are carried out. Computer simulation results show that LCAMC method, having better tracking performance than the traditional sliding mode control (SMC) system, makes the servo system track command signal quickly and accurately in spite of the persistent equivalent disturbances and ESO-LCAMC method further reduces the tracking error and filters the white noise added on the system states. Simulation results verify the robust property and comprehensive performance of control schemes. Yun-jie Wu, Yue-yang Hua, and Xiao-dong Liu Copyright © 2015 Yun-jie Wu et al. All rights reserved. Unknown Disturbance Estimation for a PMSM with a Hybrid Sliding Mode Observer Thu, 21 May 2015 09:41:48 +0000 A hybrid sliding mode observer that combines high gain feedback and a high-order sliding mode term is developed to identify the time-varying disturbance for a permanent-magnet synchronous motor (PMSM). Based on the measurable current and the position, the unknown disturbance can be identified from the sliding mode term without digital filter effect. It is then used to enhance the robustness of the speed control dynamics. For ease of implementation in real applications, such as DSP and FPGA, the proposed observer is properly designed to avoid complex mathematical operators. Simulation results are given to illustrate the performance of the proposed observer. Gang Chen, Yong Zhou, TingTing Gao, and Qicai Zhou Copyright © 2015 Gang Chen et al. All rights reserved. Nonlinear Disturbance-Observer-Based Sliding Mode Control for Flexible Air-Breathing Hypersonic Vehicles Thu, 21 May 2015 09:00:29 +0000 This paper investigates a tracking problem for flexible air-breathing hypersonic vehicles (FAHVs) with composite disturbance. The composite disturbance produced by flexible effects, parameter uncertainties, and external interferences is modeled as a kind of unknown derivative-bounded disturbance in this paper. Then a novel composite control strategy is presented for the nonlinear FAHV model with the composite disturbance, which combines a nonlinear disturbance-observer-based compensator (NDOBC) and a dynamic-inversion-based sliding mode controller (DIBSMC). Specifically, the NDOBC is constructed to estimate and compensate for the composite disturbance, and the DIBSMC is designed to track desired trajectories of velocity and flight path angle. Moreover, the uniformly ultimate boundedness of the composite system can be guaranteed by using Lyapunov theory. Finally, simulation results on a full nonlinear model of FAHVs demonstrate that the proposed nonlinear disturbance-observer-based sliding mode controller is more effective than the traditional DIBSMC. Specifically, it is shown that the chattering of traditional DIBSMC in presence of composite disturbances can be attenuated with the NDOBC. Na Wang, Xiu-Ming Yao, and Wen-Shuo Li Copyright © 2015 Na Wang et al. All rights reserved. A New SVM Multiclass Incremental Learning Algorithm Thu, 21 May 2015 07:10:35 +0000 A new support vector machine (SVM) multiclass incremental learning algorithm is proposed. To each class training sample, the hyperellipsoidal classifier that includes as many samples as possible and pushes the outlier samples away is trained in the feature space. When the new samples are added to the classification system, the algorithm reuses the old classifiers that have nothing to do with the new sample classes. To be classified sample, the Mahalanobis distances are used to decide the class of classified sample. If the sample point is not surrounded by any hyperellipsoidal or is surrounded by more than one hyperellipsoidal, the membership is used to confirm its class. The experimental results show that the algorithm has higher performance in classification precision and classification speed. Yuping Qin, Dan Li, and Aihua Zhang Copyright © 2015 Yuping Qin et al. All rights reserved. A Nonlinear Exact Disturbance Observer Inspired by Sliding Mode Techniques Thu, 21 May 2015 06:35:43 +0000 Inspired by sliding mode techniques, a nonlinear exact disturbance observer is proposed. The disturbance and its derivatives up to the second order are assumed to be bounded. However, the bounds of the disturbance and its derivatives are unknown, and they are adaptively estimated online during the observation of the disturbances. The exact convergence of the disturbance observer to the genuine disturbance is assured theoretically. The convergence speed of the disturbance estimation error is controlled by design parameters. The proposed method is robust to the type of disturbance and is easy to be implemented. Computer simulation results show the superiority and effectiveness of the proposed formulation. Xinkai Chen Copyright © 2015 Xinkai Chen. All rights reserved. A Mixed Variable Speed Reaching Law of Sliding Mode Control for Spacecraft Tracking System Wed, 20 May 2015 17:26:49 +0000 For spacecraft tracking control system, the reaching law election and controller design are two crucial and important problems. In this paper, spacecraft tracking system is considered as a discrete-time system, a mixed variable speed reaching law of SMC, and a controller for spacecraft tracking system has been investigated. Theory proves that this method can ensure the stability of spacecraft system and eliminate the chattering phenomenon. Furthermore, when spacecraft is inflicted by a certain external interference, the regulating function of neural network can ensure strong robustness of the system. Simulation results show that, compared with exponential reaching law and classical variable speed reaching law, the proposed reaching law has better suppress chattering effect and dynamic performance. Yao Zhang and Yu-Xin Zhao Copyright © 2015 Yao Zhang and Yu-Xin Zhao. All rights reserved. Quasi-Sliding Networked Control of Systems Subject to Unbounded Disturbance with Limited Rate of Change Wed, 20 May 2015 16:44:08 +0000 This paper concerns network based sliding mode control of linear plants with state measurement delay. The considered plants are subject to unbounded disturbance, but it is assumed that the change of disturbance value between each two subsequent sampling instants is limited. In order to combat the unpredictable disturbance in the environment with state measurement delay, a novel sliding mode controller has been introduced. It utilizes two nominal models of the plant to drive the system state along a desired trajectory and counteract the predicted effect of the past disturbance on the system. It has been proven that applying the new control strategy to the plant confines the system state to a defined band around the sliding hyperplane. Andrzej Bartoszewicz and Paweł Latosiński Copyright © 2015 Andrzej Bartoszewicz and Paweł Latosiński. All rights reserved. Dislocation Synchronization of the Different Complex Value Chaotic Systems Based on Single Adaptive Sliding Mode Controller Wed, 20 May 2015 16:38:24 +0000 Based on the active control and the adaptive sliding mode controller, a new method of the combination of the active control and the single adaptive sliding mode variable structure control is proposed to realize the dislocation synchronization of the three-dimensional different complex value chaotic systems. The synchronization method is suitable not only for the same complex value chaotic systems, but also for different complex value chaotic systems, so it expands the application of the single sliding mode controller. For the states in the complex space of the driving system and response system, the synchronization for the complex state of the two different chaotic systems is achieved according to the dislocation relationship, not in accordance with the corresponding relationship. The complexity of complex value chaotic system and the diversity of dislocation synchronization increase the security of the chaotic secure communication. This single adaptive sliding mode variable structure controller is simple, and it can enhance the robustness of the system. Theoretical analysis and numerical simulation prove the feasibility and effectiveness of the controller designed. Li-lian Huang, Shuai-shuai Shi, and Juan Zhang Copyright © 2015 Li-lian Huang et al. All rights reserved. Nonlinear Diversified Processes Monitoring Wed, 20 May 2015 13:48:00 +0000 The paper proposed a new method to classify and establish the monitoring model for diversified processes data with multiscale. The advantages of the proposed approach are listed as follows. (1) The issues of diversified processes data with multiscale are considered and the fault monitoring effect is enhanced. (2) From a new perspective, the common and specific characteristic subspaces are extracted to help simplify the structure of the monitoring model. (3) It makes the correlation between the common subspace itself and input-output dataset of each mode as close as possible. The effect of the proposed method has been shown in the Experiment Results section. Yunpeng Fan, Shipeng Li, Wenyou Du, and Yingwei Zhang Copyright © 2015 Yunpeng Fan et al. All rights reserved. Multivariable Super Twisting Based Robust Trajectory Tracking Control for Small Unmanned Helicopter Wed, 20 May 2015 13:47:07 +0000 This paper presents a highly robust trajectory tracking controller for small unmanned helicopter with model uncertainties and external disturbances. First, a simplified dynamic model is developed, where the model uncertainties and external disturbances are treated as compounded disturbances. Then the system is divided into three interconnected subsystems: altitude subsystem, yaw subsystem, and horizontal subsystem. Second, a disturbance observer based controller (DOBC) is designed based upon backstepping and multivariable super twisting control algorithm to obtain robust trajectory tracking property. A sliding mode observer works as an estimator of the compounded disturbances. In order to lessen calculative burden, a first-order exact differentiator is employed to estimate the time derivative of the virtual control. Moreover, proof of the stability of the closed-loop system based on Lyapunov method is given. Finally, simulation results are presented to illustrate the effectiveness and robustness of the proposed flight control scheme. Xing Fang, Aiguo Wu, Yujia Shang, and Chunyan Du Copyright © 2015 Xing Fang et al. All rights reserved. Finite-Time Reentry Attitude Control Using Time-Varying Sliding Mode and Disturbance Observer Wed, 20 May 2015 13:45:44 +0000 This paper presents the finite-time attitude control problem for reentry vehicle with redundant actuators in consideration of planet uncertainties and external disturbances. Firstly, feedback linearization technique is used to cancel the nonlinearities of equations of motion to construct a basic mode for attitude controller. Secondly, two kinds of time-varying sliding mode control methods with disturbance observer are integrated with the basic mode in order to enhance the control performance and system robustness. One method is designed based on boundary layer technique and the other is a novel second-order sliding model control method. The finite-time stability analyses of both resultant closed-loop systems are carried out. Furthermore, after attitude controller produces the torque commands, an optimization control allocation approach is introduced to allocate them into aerodynamic surface deflections and on-off reaction control system thrusts. Finally, the numerical simulation results demonstrate that both of the time-varying sliding mode control methods are robust to uncertainties and disturbances without chattering phenomenon. Moreover, the proposed second-order sliding mode control method possesses better control accuracy. Xuzhong Wu, Shengjing Tang, Jie Guo, and Yao Zhang Copyright © 2015 Xuzhong Wu et al. All rights reserved. Application of Base Force Element Method on Complementary Energy Principle to Rock Mechanics Problems Wed, 20 May 2015 12:01:18 +0000 The four-mid-node plane model of base force element method (BFEM) on complementary energy principle is used to analyze the rock mechanics problems. The method to simulate the crack propagation using the BFEM is proposed. And the calculation method of safety factor for rock mass stability was presented for the BFEM on complementary energy principle. The numerical researches show that the results of the BFEM are consistent with the results of conventional quadrilateral isoparametric element and quadrilateral reduced integration element, and the nonlinear BFEM has some advantages in dealing crack propagation and calculating safety factor of stability. Yijiang Peng, Qing Guo, Zhaofeng Zhang, and Yanyan Shan Copyright © 2015 Yijiang Peng et al. All rights reserved. A Conforming Triangular Plane Element with Rotational Degrees of Freedom Wed, 20 May 2015 11:39:20 +0000 This paper presents a novel way to formulate the triangular plane element with rotational degrees of freedom (RDOF). The linear distribution of rotational displacement is assumed. The conforming displacement along the sides based on the rotational displacement assumption is derived, and the triangular plane element TR3 for isotropic material is formulated. By using the explicit integral formulae of the triangular element, the matrices used in the proposed plane element TR3 are calculated efficiently. The benchmark examples showed thier high accuracy and high efficiency. Xiang-Rong Fu, Ming-Wu Yuan, and Chen Pu Copyright © 2015 Xiang-Rong Fu et al. All rights reserved. Intelligent Autofeedback and Safety Early-Warning for Underground Cavern Engineering during Construction Based on BP Neural Network and FEM Wed, 20 May 2015 11:38:41 +0000 The low efficiency of feedback analysis is one of the main shortcomings in the construction of underground cavern engineering. With this in mind, a method of intelligent autofeedback and safety early-warning for underground cavern is proposed based on BP neural network and FEM. The training sample points are chosen by using uniform test design method, and the autogeneration of FEM calculation file for ABAQUS is realized by using the technique of file partition, information grouping, and orderly numbering. Then, intelligent autoinversion of mechanics parameters is realized, and the automatic connection of parameter inversion, subsequent prediction, and safety early-warning is achieved. The software of intelligent autofeedback and safety early-warning for underground cavern engineering during construction is developed. Finally, the applicability of the proposed method and the developed software is verified through an application example of underground cavern of a pumped-storage power station located in Southwest China. Lei Xu, Taijun Zhang, and Qingwen Ren Copyright © 2015 Lei Xu et al. All rights reserved. Symmetry Properties of Optimal Relative Orbit Trajectories Wed, 20 May 2015 11:21:42 +0000 The determination of minimum-fuel or minimum-time relative orbit trajectories represents a classical topic in astrodynamics. This work illustrates some symmetry properties that hold for optimal relative paths and can considerably simplify their determination. The existence of symmetry properties is demonstrated in the presence of certain boundary conditions for the problems of interest, described by the linear Euler-Hill-Clohessy-Wiltshire equations of relative motion. With regard to minimum-fuel paths, the primer vector theory predicts the existence of several powered phases, divided by coast arcs. In general, the optimal thrust sequence and duration depend on the time evolution of the switching function. In contrast, a minimum-time trajectory is composed of a single continuous-thrust phase. The first symmetry property concerns minimum-fuel and minimum-time orbit paths, both in two and in three dimensions. The second symmetry property regards minimum-fuel relative trajectories. Several examples illustrate the usefulness of these properties in determining minimum-time and minimum-fuel relative paths. Mauro Pontani Copyright © 2015 Mauro Pontani. All rights reserved. SINS/CNS Nonlinear Integrated Navigation Algorithm for Hypersonic Vehicle Wed, 20 May 2015 11:19:32 +0000 Celestial Navigation System (CNS) has characteristics of accurate orientation and strong autonomy and has been widely used in Hypersonic Vehicle. Since the CNS location and orientation mainly depend upon the inertial reference that contains errors caused by gyro drifts and other error factors, traditional Strap-down Inertial Navigation System (SINS)/CNS positioning algorithm setting the position error between SINS and CNS as measurement is not effective. The model of altitude azimuth, platform error angles, and horizontal position is designed, and the SINS/CNS tightly integrated algorithm is designed, in which CNS altitude azimuth is set as measurement information. GPF (Gaussian particle filter) is introduced to solve the problem of nonlinear filtering. The results of simulation show that the precision of SINS/CNS algorithm which reaches 130 m using three stars is improved effectively. Yong-jun Yu, Jin-fa Xu, and Zhi Xiong Copyright © 2015 Yong-jun Yu et al. All rights reserved. Sensor Fault Tolerant Control of a Fast Steering Mirror System Using Adaptive PI-Based Sliding Mode Observer and Hardware Redundancy Wed, 20 May 2015 11:15:47 +0000 The aim of this paper is to present a sensor fault-tolerant control (FTC) scheme for a two-axis fast steering mirror (FSM) system with minimum power consumption and without changing the controller structure. In this paper, an adaptive PI-based sliding mode observer (APISMO) is adopted firstly to estimate the fault signal, which does not require any prior knowledge of the fault. The estimation is then used by the fault isolation logic to identify the fault. The redundant sensor would be powered up to replace the faulty one when faults occur. During the backup sensor booting up, for maintaining the normal performance of the closed-loop system approximately, a fault-free estimation of the position provided by the APISMO is used as feedback signal. Experimental studies on a prototype system show that the proposed APISMO can effectively reconstruct the fault signals even when the two primary position sensors are faulty simultaneously. Meanwhile, the effectiveness and performance of the proposed scheme have been verified. Hongju Wang, Qiliang Bao, Wenshu Yang, Zidong Liu, and Jing Tian Copyright © 2015 Hongju Wang et al. All rights reserved.