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The purpose of this paper is to study a finite‐thrust orbital transfer optimization problem via a new optimal control method‐Gauss pseudospectral method.

Based on the dynamic equations with the pseudo‐equinoctial elements as state variable, optimality condition is derived and the optimization problem is converted into nonlinear programming problem. Gauss pseudospectral method is used to avoid the two‐point boundary value problem. The dynamic equations are converted into static parameter optimization problem. The state variables and control variables are selected as optimal parameters at all collocation nodes. Two numerical examples of orbital transfer with coplanar and different planes are analyzed, respectively.

The simulation results demonstrate that Gauss pseudospectral method is not sensitive to the initial conditions of orbital transfer. They also show good robustness and control facility.

The precision and efficiency of this trajectory optimization method are demonstrated by applying it to space vehicle orbital transfer with finite thrust optimization problem.

The research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The paper describes the methodology, and gives illustrative results for simple geometries.

The pseudospectral matrix element method of discretisation is selected as the basis for the CFD technique adopted, because of its high spectral accuracy. It is implemented as a means of solving the Navier‐Stokes equations coupled with the modified compressibility method.

The viscous solver has been validated for the benchmark cases of uniform flow past a cylinder at a Reynolds number of 40, and 2D cavity flows. Results for sloshing of a viscous fluid in a tank have been successfully compared with those from a linearised analytical solution. Application of the method is illustrated by the results for the interaction of an impulsive wave with a surface piercing circular cylinder in a cylindrical tank.

The paper demonstrates the viability of the approach adopted. The limitation of small amplitude waves should be tackled in future work.

The results will have particular significance in the context of validating computations from more complex schemes applicable to arbitrary geometries.

The new methodology and results are of interest to the community of those developing numerical models of flow past marine structures.

The purpose of this paper is to develop pseudospectral meshless radial point Hermit interpolation (PSMRPHI) for applying to the Motz problem.

The author aims to propose a kind of PSMRPHI method.

Based on the Motz problem, the author aims also to compare PSMRPHI and PSMRPI which belong to more influence type of meshless methods.

Although the PSMRPHI method has been infrequently used in applications, the author proves it is more accurate and trustworthy than the PSMRPI method.

The purpose of this paper is to plan the penetration trajectory for unmanned aerial vehicle (UAV) in the presence of radar‐guided surface to air missiles (SAMs).

The penetration trajectory planning problem is modelled based on four aspects of radar tracking features. As penetration just utilizes the low observability of radar cross section (RCS) to satisfy temporal constraints of tracking, the problem is formulated as multi‐phase trajectory planning with detected probability (MTP‐DP). While utilizing both the low observability of RCS and the radial velocity blind area of radar, the problem is formulated as multi‐phase trajectory planning with detected probability and radial velocity (MTP‐DP&RV). The pseudospectral multi‐phase optimal control based trajectory planning algorithm is proposed.

The results of the examples illustrate that the multi‐phase trajectory planning method can finely utilize the radar tracking features to optimize the comprehensive efficiency of penetration. The pseudospectral multi‐phase optimal control based trajectory planning algorithm could effectively solve the trajectory planning problem.

This paper provides new structured method to plan UAV penetration trajectory for military application and academic study.

This study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them have been presented.

In this article, the authors apply the method of lines (MOL) together with the pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative (SFPDEs). Then, using the collocation nodes to reduce the SFPDEs to the system of ordinary differential equations, which can be solved by the ode45 MATLAB toolbox.

Applying the MOL method together with the pseudospectral discretization method converts the space-dependent on fractional partial differential equations to the system of ordinary differential equations.

This paper contributes to gain choosing the shifted Jacobi functions basis with special parameters a, b and give the authors this opportunity to obtain the left- and right-sided fractional differentiation matrices for this basis exactly. The results of the examples are presented in this article. The authors found that the method is efficient and provides accurate results, and the authors found significant implications for success in the science, technology, engineering and mathematics domain.

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem.

A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently.

Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory.

Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm.

The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.

This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source.

The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method.

The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted.

The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

The purpose of the paper is to study the variation of optimal burnout angle at the end of the ascent phase and the optimal control deflection during the glide phase, that would maximize the downrange performance of a hypersonic boost-glide waverider, with variation in heat rate and integrated heat load limit.

The approach used is to model the boost phase so as to optimize the burnout conditions. The nonlinear, multiphase, constraint optimal control problem is solved using an hp-adaptive pseudospectral method.

The constraint heat load results for the waverider configuration reveal that the integrated heat load can be reduced by more than half with only 10 per cent penalty in the overall downrange of the hypersonic boost-glide vehicle, within a burnout speed range of 3.7 to 4.3 km/s. The angle-of-attack trim control requirements increase with stringent heat rate and integrated heat load bounds. The normal acceleration remains within limits.

The trajectory results imply lower thermal protection system weight because of reduced heat load trajectory profile and therefore lower thermal protection system cost.

The research provides further study on the trajectory design to the hypersonic boost-glide vehicles for medium range application.

This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation.

Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method.

It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels.

In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.

The purpose of this paper is to investigate the time optimal trajectory of the multi-tethered robot (MTR) on a large spinning net structures in microgravity environment.

The MTR is a small space robot that uses several tethers attached to the corner-fixed satellites of a spinning net platform. The transition of the MTR from a start point to any arbitrary designated points on the platform surface can be achieved by controlling the tethers’ length and tension simultaneously. Numerical analysis of trajectory optimization problem for the MTR is implemented using the pseudospectral (PS) method.

The globally time optimal trajectory for MTR on a free-end spinning net platform can be obtained through the PS method.

The analysis in this paper is limited to a planar trajectory and the effects caused by attitude of the MTR will be neglected. To make the problem simple and to see the feasibility in the general case, in this paper, it is assumed there are no any limitations of mechanical hardware constraints such as the velocity limitation of the robot and tether length changing constraint, while only geometrical constraints are considered.

The optimal solution derived from numerical analysis can be used for a path planning, guidance and navigation control. This method can be used for more efficient on-orbit autonomous self-assembly system or extravehicular activities supports which using a tether-controlled robot.

This approach for a locomotion mechanism has the capability to solve problems of conventional crawling type robots on a loose net in microgravity.