While there is a strong current interest in and an increasing body of the latest numerical work on fuel-optimal powered descent inside an atmosphere, little recent analytical understanding of the problem has been reported. This paper analyzes the endo-atmospheric fuel-optimal rocket landing problem in three-dimensional motion. The necessary conditions for the problem that account for both propulsive and aerodynamic forces are derived. They include the full set of costate equations and the optimality conditions of the body attitude in terms of the angle of attack and sideslip angle. In contrast to a long-standing assumption of coordinated flight in the literature, it is shown that in general coordinated flight is not optimal if sideslip modulation is allowed. Special cases, such as small-angle and in-plane motion, are analyzed and harmonized with the previous results that are well known in the literature. The analytical conditions derived in this paper can also serve as independent verification for numerical solutions obtained by direct methods in optimal control or can be exploited for trajectory-design purposes.

Broomcorn millet (Panicum miliaceum L.) is one of the earliest domesticated crops in the world. Weedy broomcorn millet [Panicum ruderale (Kitag.) Chang or Panicum miliaceum subsp. ruderale (Kitag.) Tzvel] is thought to be the descendant of the wild ancestor or the feral type of this cereal. The genealogical relationships and genetic divergence among these taxa have not been clarified. In this study, the genetic diversity and population structure of weedy and cultivated broomcorn millets were investigated by using the high-throughput sequencing technology, i.e., the specific-locus amplified fragment sequencing (SLAF-seq). Our analyses consistently revealed both the wild and the feral genotypes in the weedy broomcorn millets. The single nucleotide polymorphisms (SNPs) at the genomic level provided useful evidence to distinguish the wild and the endoferal/exoferal types of weedy broomcorn millets. The genetic divergence revealed between the cultivated broomcorn millet from eastern Eurasia and those from central-western Eurasia was probably derived from either the genetic introgression from weedy broomcorn millets along the spread routes or the founder effect, while the limited gene flow of broomcorn millets from eastern and central-western Eurasia was probably due to the different uses of broomcorn millets and eating habits of the local people.

Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the difficulty of guessing the adjoint variables. This paper proposes two learning-based approaches to find the initial guess of adjoint variables in real-time, which can be applied to solve general TPBVPs. For cases with database of solutions and corresponding adjoint variables of a TPBVP under varying boundary conditions, a supervised learning method is applied to learn the HJB solutions off-line. After obtaining a trained neural network from supervised learning, we are able to find proper initial adjoint variables for given boundary conditions in real-time. However, when validated solutions of TPBVPs are not available, the reinforcement learning method is applied to solve HJB by constructing a neural network, defining a reward function, and setting appropriate super parameters. The reinforcement learning based HJB method can learn how to find accurate adjoint variables via an updating neural network. Finally, both learning approaches are implemented in classical optimal control problems to verify the effectiveness of the learning based HJB methods.

Many optimal control problems can be cast into polynomial optimization problems through the discretization and conversion of expressions. The polynomial programming problem can further be transformed into a general quadratically constrained quadratic programing (QCQP) problem by introducing new variables and equality constraints. This paper develops an alternating minimization algorithm (AMA) to search for the optimal solution to a QCQP that is formulated as a rank-one constrained optimization problem. Based on the fact that a rank-one matrix is formed by two equivalent vectors, AMA alternatively solves each vector in sequence. Each sequential problem is a convex quadratic programming problem with linear constraints. A convergence analysis of AMA is provided. The efficacy of the proposed AMA is demonstrated by numerically solving two constrained optimal control problems where the conventional approach based on nonlinear programming experiences difficulty.

The mechanism of mercury oxidation/adsorption on an NH4Br modified fly ash (NH4Br-FA) was discussed. The effect of flue gas component including O2, SO2 and NO, and the roles of main fly ash compositions on the Hg0 oxidation/adsorption capability by the NH4Br-FA was evaluated on a fixed-bed reactor. The mercury adsorption species on the spent sorbent were then identified by the temperature programmed decomposition desorption (TPDD) method. The results show that NH4Br modification on the fly ash not only improves Hg0 oxidation, but also promotes Hg0 adsorption. Due to the generation of Br-containing functional groups, HgBr2 is the main adsorption form on the surface of the NH4Br-FA. O2 cannot promote Hg0 oxidation or adsorption, but leads to the generation of little HgO. NO cannot promotes Hg0 oxidation, while significantly improves the Hg0 adsorption on the NH4Br-FA with the adsorbate of HgBr2, HgO or Hg2(NO3)2. SO2 has little effect on Hg0 oxidation, but significantly inhibits Hg0 adsorption on the surface of the NH4Br-FA, because SO2 can destroy the Br activate sites leading to deactivation, in which there is no HgS or HgSO4 formation. The main metal oxides in the NH4Br-FA include Fe2O3, TiO2, CaO, and Al2O3, which display poor mercury removal capability. However, after the modification of NH4Br solution, the NH4Br-Fe2O3 and the NH4Br-TiO2 demonstrate excellent Hg0 oxidation capability with poor Hg0 adsorption performance.

Convex optimization has found wide applications in recent years due to its unique theoretical advantages and the polynomial-time complexity of state-of-the-art solution algorithms for convex programming. This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight. The foremost challenge in applying convex optimization in most aerospace engineering problems lies in the nonlinearity and nonconvexity of the problem. Exclusive reliance on linearization does not always work well, as is the case in entry trajectory optimization. This paper focuses on how to formulate realistic, highly constrained entry trajectory optimization problems in a fashion suitable to be solved by second-order cone programming with a combination of successive linearization and relaxation techniques. Rigorous analysis is conducted to support the soundness of the approach. Numerical demonstrations are provided to show the efficacy and effectiveness of the proposed method.

This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.

The homotopy method has long served as a useful tool in solving optimal control problems, particularly highly nonlinear and sensitive ones for which good initial guesses are difficult to obtain, such as some of the well-known problems in aerospace trajectory optimization. However, the traditional homotopy method often fails midway: a fact that occasional practitioners are not aware of, and a topic which is rarely investigated in aerospace engineering. This paper first reviews the main reasons why traditional homotopy fails. A new double-homotopy method is developed to address the common failures of the traditional homotopy method. In this approach, the traditional homotopy is employed until it encounters a difficulty and stops moving forward. Another homotopy originally designed for finding multiple roots of nonlinear equations takes over at this point, and it finds a different solution to allow the traditional homotopy to continue on. This process is repeated whenever necessary. The proposed method overcomes some of the frequent difficulties of the traditional homotopy method. Numerical demonstrations in a nonlinear optimal control problem and a three-dimensional low-thrust orbital transfer problem are presented to illustrate the applications of the method.

The polynomial optimal control problems (POCPs) have many applications where the objective, dynamics, and constraints are represented by polynomial functions. Through discretization, a POCP can be transformed into a polynomial programming problem. Very few of such problems are convex and thus they are generally classi ed as NP-hard. In this paper, we rst introduce new variables to transform the polynomial objective and/or constraints into quadratic functions to obtain an equivalent formulation of Quadratically Constrained Quadratic Programming (QCQP) problem. Further transformation to matrix linear programming problem with rank-one constraint on the unknown matrix. A successive convex optimization approach, named Iterative Rank Minimization (IRM), is proposed to gradually satisfy the rank constraint. Rigorous proof is provided to verify that IRM can guarantee converging to an optimum of the original problem. The optimal launch ascent problem is solved by the proposed method to verify the e ectiveness and improved performance of the proposed algorithm compared to the results in the literature.

While numerical predictor-corrector entry guidance algorithms have in recent years demonstrated great potential, a standing concern still is that the computational requirement such an algorithm demands may exceed the capability of the flight computer. An alternate entry guidance method combining a fullynumerical predictor-corrector algorithm with Linear Quadratic Regulator (LQR) based trajectory tracking control is explored in this paper. The predictor-corrector algorithm is used to plan a reference trajectory onboard. This reference trajectory is then tracked by an LQR tracking law, which provides the guidance commands. When necessary, the reference trajectory is updated periodically by the predictor-corrector algorithm with respect to the current vehicle state to eliminate any accumulated tracking error. The effectiveness of the LQR gains has been known and is demonstrated again in this paper to be independent of the particular reference trajectory used to generate them. Therefore a set of LQR gains can be generated offline, and stored online for tracking any reference trajectory planned by the predictor-corrector algorithm. Such an entry guidance strategy significantly reduces onboard computational requirements and still retains the adaptability of a numerical predictor-corrector entry guidance algorithm. The implementation details are presented. Numerical results are provided to demonstrate the effectiveness of the proposed method.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

The maximum-crossrange problem is an optimal control problem of computing the maximum crossrange reachable by a hypersonic entry vehicle at a specified downrange, which has long known to be very difficult to solve due to its high nonlinearities and non-convexity. This paper presents how to convexify the problem so that it can be efficiently solved by successive second-order cone programming (SOCP). Particular focus is given on equivalent transformation of the original optimization objective and rigorous establishment of validity of the relaxation process used for convexification. In addition, it is observed that iteratively solving the SOCP problems may not always guarantee convergence to the original problem, a simple line search approach is proposed which is found critical to ensure the convergence of the successive SOCP method. Numerical demonstrations are provided to illustrate the effectiveness and efficiency of the proposed method and its applicability to both orbital and suborbital missions.