265,466 research outputs found
Interception and deviation of near Earth objects via solar collector strategy
A solution to the asteroid deviation problem via a low-thrust strategy is proposed. This formulation makes use of the proximal motion equations and a semi-analytical solution of the Gauss planetary equations. The average of the variation of the orbital elements is computed, together with an approximate expression of their periodic evolution. The interception and the deflection phase are optimised together through a global search. The low-thrust transfer is preliminary designed with a shape based method; subsequently the solutions are locally refined through the Differential Dynamic Programming approach. A set of optimal solutions are presented for a deflection mission to Apophis, together with a representative trajectory to Apophis including the Earth escape
Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization
Dual decomposition has been successfully employed in a variety of distributed
convex optimization problems solved by a network of computing and communicating
nodes. Often, when the cost function is separable but the constraints are
coupled, the dual decomposition scheme involves local parallel subgradient
calculations and a global subgradient update performed by a master node. In
this paper, we propose a consensus-based dual decomposition to remove the need
for such a master node and still enable the computing nodes to generate an
approximate dual solution for the underlying convex optimization problem. In
addition, we provide a primal recovery mechanism to allow the nodes to have
access to approximate near-optimal primal solutions. Our scheme is based on a
constant stepsize choice and the dual and primal objective convergence are
achieved up to a bounded error floor dependent on the stepsize and on the
number of consensus steps among the nodes
Mitigating the Curse of Dimensionality: Sparse Grid Characteristics Method for Optimal Feedback Control and HJB Equations
We address finding the semi-global solutions to optimal feedback control and
the Hamilton--Jacobi--Bellman (HJB) equation. Using the solution of an HJB
equation, a feedback optimal control law can be implemented in real-time with
minimum computational load. However, except for systems with two or three state
variables, using traditional techniques for numerically finding a semi-global
solution to an HJB equation for general nonlinear systems is infeasible due to
the curse of dimensionality. Here we present a new computational method for
finding feedback optimal control and solving HJB equations which is able to
mitigate the curse of dimensionality. We do not discretize the HJB equation
directly, instead we introduce a sparse grid in the state space and use the
Pontryagin's maximum principle to derive a set of necessary conditions in the
form of a boundary value problem, also known as the characteristic equations,
for each grid point. Using this approach, the method is spatially causality
free, which enjoys the advantage of perfect parallelism on a sparse grid.
Compared with dense grids, a sparse grid has a significantly reduced size which
is feasible for systems with relatively high dimensions, such as the -D
system shown in the examples. Once the solution obtained at each grid point,
high-order accurate polynomial interpolation is used to approximate the
feedback control at arbitrary points. We prove an upper bound for the
approximation error and approximate it numerically. This sparse grid
characteristics method is demonstrated with two examples of rigid body attitude
control using momentum wheels
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