Millennial Variability in an Idealized Ocean Model: Predicting the AMOC Regime Shifts

A salient feature of paleorecords of the last glacial interval in the North Atlantic is pronounced millennial variability, commonly known as Dansgaard–Oeschger events. It is believed that these events are related to variations in the Atlantic meridional overturning circulation and heat transport. Here, the authors formulate a new low-order model, based on the Howard–Malkus loop representation of ocean circulation, capable of reproducing millennial variability and its chaotic dynamics realistically. It is shown that even in this chaotic model changes in the state of the meridional overturning circulation are predictable. Accordingly, the authors define two predictive indices which give accurate predictions for the time the circulation should remain in the on phase and then stay in the subsequent off phase. These indices depend mainly on ocean stratification and describe the linear growth of small perturbations in the system. Thus, monitoring particular indices of the ocean state could help predict a potential shutdown of the overturning circulation

Perturbations of time optimal control problems for a class of abstract parabolic systems

In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application to PDEs systems concerns the behavior of optimal time and of the associated optimal controls for parabolic equations with highly oscillating coefficients, as we encounter in homogenization theory. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the solutions of the time optimal control problems for the systems with oscillating coefficients converge, in the usual norms, to the solution of the corresponding problem for the homogenized system. In order to prove our main theorem, we provide several new results, which could be of a broader interest, on time and norm optimal control problems

Investigation of Direct Force Control for Planetary Aerocapture at Neptune

In this work, a direct force control numerical predictor-corrector guidance architecture is developed to enable Neptune aerocapture using flight-heritage blunt body aeroshells. A linear aerodynamics model is formulated for a Mars Science Laboratory-derived aeroshell. The application of calculus of variations shows that the optimal angle of attack and side-slip angle control laws are bang-bang. A closed-loop numerical predictor-corrector direct force control guidance algorithm is developed and numerically simulated using the Program to Optimize Simulated Trajectories II. The Monte Carlo simulated trajectories are demonstrated to be robust to the modeled dispersions in aerodynamics, atmospheric density, and entry state. An aerocapture technology trade study demonstrates that blunt body direct force control aerocapture enables similar performance as slender body bank angle control but halves the peak g-loading

On-board Trajectory Computation for Mars Atmospheric Entry Based on Parametric Sensitivity Analysis of Optimal Control Problems

This thesis develops a precision guidance algorithm for the entry of a small capsule into the atmosphere of Mars. The entry problem is treated as nonlinear optimal control problem and the thesis focuses on developing a suboptimal feedback law. Therefore parametric sensitivity analysis of optimal control problems is combined with dynamic programming. This approach enables a real-time capable, locally suboptimal feedback scheme. The optimal control problem is initially considered in open loop fashion. To synthesize the feedback law, the optimal control problem is embedded into a family of neighboring problems, which are described by a parameter vector. The optimal solution for a nominal set of parameters is determined using direct optimization methods. In addition the directional derivatives (sensitivities) of the optimal solution with respect to the parameters are computed. Knowledge of the nominal solution and the sensitivities allows, under certain conditions, to apply Taylor series expansion to approximate the optimal solution for disturbed parameters almost instantly. Additional correction steps can be applied to improve the optimality of the solution and to eliminate errors in the constraints. To transfer this strategy to the closed loop system, the computation of the sensitivities is performed with respect to different initial conditions. Determining the perturbation direction and interpolating between sensitivities of neighboring initial conditions allows the approximation of the extremal field in a neighborhood of the nominal trajectory. This constitutes a locally suboptimal feedback law. The proposed strategy is applied to the atmospheric entry problem. The developed algorithm is part of the main control loop, i.e. optimal controls and trajectories are computed at a fixed rate, taking into account the current state and parameters. This approach is combined with a trajectory tracking controller based on the aerodynamic drag. The performance and the strengthsa and weaknesses of this two degree of freedom guidance system are analyzed using Monte Carlo simulation. Finally the real-time capability of the proposed algorithm is demonstrated in a flight representative processor-in-the-loop environment

Boundary conditions control for a Shallow-Water model

A variational data assimilation technique was used to estimate optimal discretization of interpolation operators and derivatives in the nodes adjacent to the rigid boundary. Assimilation of artificially generated observational data in the shallow-water model in a square box and assimilation of real observations in the model of the Black sea are discussed. It is shown in both experiments that controlling the discretization of operators near a rigid boundary can bring the model solution closer to observations as in the assimilation window and beyond the window. This type of control allows also to improve climatic variability of the model.Comment: arXiv admin note: substantial text overlap with arXiv:1112.4293, arXiv:1112.3503, arXiv:0905.470