Solar sail capture trajectories at Mercury

Mercury is an ideal environment for future planetary exploration by solar sail since it has proved difficult to reach with conventional propulsion and hence remains largely unexplored. In addition, its proximity to the Sun provides a solar sail acceleration of order ten times the sail characteristic acceleration at 1 AU. Conventional capture techniques are shown to be unsuitable for solar sails and a new method is presented. It is shown that capture is bound by upper and lower limits on the orbital elements of the approach orbit and that failure to be within limits results in a catastrophic collision with the planet. These limits are presented for a range of capture inclinations and sail characteristic accelerations. It is found that sail hyperbolic excess velocity is a critical parameter during capture at Mercury, with only a narrow allowed band in order to avoid collision with the planet. The new capture methodis demonstrated for a Mercury sample return mission

Dissipative boundary conditions for nonlinear 1-D hyperbolic systems: sharp conditions through an approach via time-delay systems

We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known weaker sufficient condition for exponential stability with respect to the H^2-norm is not sufficient for the exponential stability with respect to the C^1-norm. Hence, due to the nonlinearity, even in the case of classical solutions, the exponential stability depends strongly on the norm considered. We also give a new sufficient condition for the exponential stability with respect to the W^{2,p}-norm. The methods used are inspired from the theory of the linear time-delay systems and incorporate the characteristic method

Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model

The Aw-Rascle-Zhang (ARZ) model can be interpreted as a generalization of the Lighthill-Whitham-Richards (LWR) model, possessing a family of fundamental diagram curves, each of which represents a class of drivers with a different empty road velocity. A weakness of this approach is that different drivers possess vastly different densities at which traffic flow stagnates. This drawback can be overcome by modifying the pressure relation in the ARZ model, leading to the generalized Aw-Rascle-Zhang (GARZ) model. We present an approach to determine the parameter functions of the GARZ model from fundamental diagram measurement data. The predictive accuracy of the resulting data-fitted GARZ model is compared to other traffic models by means of a three-detector test setup, employing two types of data: vehicle trajectory data, and sensor data. This work also considers the extension of the ARZ and the GARZ models to models with a relaxation term, and conducts an investigation of the optimal relaxation time.Comment: 30 pages, 10 figures, 3 table

Control of functional differential equations with function space boundary conditions

Problems involving functional differential equations with terminal conditions in function space are considered. Their application to mechanical and electrical systems is discussed. Investigations of controllability, existence of optimal controls, and necessary and sufficient conditions for optimality are reported

Boundary Control of Coupled Reaction-Advection-Diffusion Systems with Spatially-Varying Coefficients

Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and spatially-varying coefficients is challenging due to complex boundary conditions that appear in the equations verified by the control kernels. In this paper we address this issue by showing that these equations are essentially equivalent to those verified by the control kernels for first-order hyperbolic coupled systems, which were recently found to be well-posed. The result therefore applies in this case, allowing us to prove H^1 stability for the closed-loop system. It also shows an interesting connection between backstepping kernels for coupled parabolic and hyperbolic problems.Comment: Submitted to IEEE Transactions on Automatic Contro