21,484 research outputs found
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
A Better Alternative to Piecewise Linear Time Series Segmentation
Time series are difficult to monitor, summarize and predict. Segmentation
organizes time series into few intervals having uniform characteristics
(flatness, linearity, modality, monotonicity and so on). For scalability, we
require fast linear time algorithms. The popular piecewise linear model can
determine where the data goes up or down and at what rate. Unfortunately, when
the data does not follow a linear model, the computation of the local slope
creates overfitting. We propose an adaptive time series model where the
polynomial degree of each interval vary (constant, linear and so on). Given a
number of regressors, the cost of each interval is its polynomial degree:
constant intervals cost 1 regressor, linear intervals cost 2 regressors, and so
on. Our goal is to minimize the Euclidean (l_2) error for a given model
complexity. Experimentally, we investigate the model where intervals can be
either constant or linear. Over synthetic random walks, historical stock market
prices, and electrocardiograms, the adaptive model provides a more accurate
segmentation than the piecewise linear model without increasing the
cross-validation error or the running time, while providing a richer vocabulary
to applications. Implementation issues, such as numerical stability and
real-world performance, are discussed.Comment: to appear in SIAM Data Mining 200
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Importance of Clipping in Neurocontrol by Direct Gradient Descent on the Cost-to-Go Function and in Adaptive Dynamic Programming
In adaptive dynamic programming, neurocontrol and reinforcement learning, the
objective is for an agent to learn to choose actions so as to minimise a total
cost function. In this paper we show that when discretized time is used to
model the motion of the agent, it can be very important to do "clipping" on the
motion of the agent in the final time step of the trajectory. By clipping we
mean that the final time step of the trajectory is to be truncated such that
the agent stops exactly at the first terminal state reached, and no distance
further. We demonstrate that when clipping is omitted, learning performance can
fail to reach the optimum; and when clipping is done properly, learning
performance can improve significantly.
The clipping problem we describe affects algorithms which use explicit
derivatives of the model functions of the environment to calculate a learning
gradient. These include Backpropagation Through Time for Control, and methods
based on Dual Heuristic Dynamic Programming. However the clipping problem does
not significantly affect methods based on Heuristic Dynamic Programming,
Temporal Differences or Policy Gradient Learning algorithms. Similarly, the
clipping problem does not affect fixed-length finite-horizon problems
A study of digital techniques for signal processing Semiannual status report, 1 Feb. - 31 Jul. 1970
Adaptive array processing, dynamic programming, digital data transmission, recursive adaptive equalizers, and finite memory communication system
A study of digital techniques for signal processing
Analysis and definition of digital techniques for signal processin
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