Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution

Extent and Causes of Chesapeake Bay Warming

Coastal environments such as the Chesapeake Bay have long been impacted by eutrophication stressors resulting from human activities, and these impacts are now being compounded by global warming trends. However, there are few studies documenting long-term estuarine temperature change and the relative contributions of rivers, the atmosphere, and the ocean. In this study, Chesapeake Bay warming, since 1985, is quantified using a combination of cruise observations and model outputs, and the relative contributions to that warming are estimated via numerical sensitivity experiments with a watershed–estuarine modeling system. Throughout the Bay’s main stem, similar warming rates are found at the surface and bottom between the late 1980s and late 2010s (0.02 +/- 0.02C/year, mean +/- 1 standard error), with elevated summer rates (0.04 +/- 0.01C/year) and lower rates of winter warming (0.01 +/- 0.01C/year). Most (~85%) of this estuarine warming is driven by atmospheric effects. The secondary influence of ocean warming increases with proximity to the Bay mouth, where it accounts for more than half of summer warming in bottom waters. Sea level rise has slightly reduced summer warming, and the influence of riverine warming has been limited to the heads of tidal tributaries. Future rates of warming in Chesapeake Bay will depend not only on global atmospheric trends, but also on regional circulation patterns in mid-Atlantic waters, which are currently warming faster than the atmosphere. Supporting model data available at: https://doi.org/10.25773/c774-a36

Cross-country sailflight as a dynamic optimization problem

A minimum-time, thermal-to-thermal sailplane trajectory optimization problem is formulated as a non-linear optimal control problem. Numerical solutions are obtained using a gradiaent projection algorithm which incorporates conjugate directions of search. Further insight into the nature of the solutions and the computational process is ontained through an analysis of the linearized sailplane dynamics and the necessary conditions for optimality. Numerical results are presented for two sailplane types and various values of thermal strength and distance between thermals. An additional problem is formulated and solved for the case of bounded control rate

Optimal topology design of structures under dynamic loads

When elastic structures are subjected to dynamic loads, a propagation problem is considered to predict structural transient response. To achieve better dynamic performance, it is important to establish an optimum structural design method. Previous work focused on minimizing the structural weight subject to dynamic constraints on displacement, stress, frequency, and member size. Even though these methods made it possible to obtain the optimal size and shape of a structure, it is necessary to obtain an optimal topology for a truly optimal design. In this paper, the homogenization design method is utilized to generate the optimal topology for structures and an explicit direct integration scheme is employed to solve the linear transient problems. The optimization problem is formulated to find the best configuration of structures that minimizes the dynamic compliance within a specified time interval. Examples demonstrate that the homogenization design method can be extended to the optimal topology design method of structures under impact loads.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46080/1/158_2005_Article_BF01195945.pd