6,670 research outputs found
Optimal trajectory generation in ocean flows
In this paper it is shown that Lagrangian Coherent
Structures (LCS) are useful in determining near optimal
trajectories for autonomous underwater gliders in a dynamic
ocean environment. This opens the opportunity for optimal
path planning of autonomous underwater vehicles by studying
the global flow geometry via dynamical systems methods. Optimal
glider paths were computed for a 2-dimensional kinematic
model of an end-point glider problem. Numerical solutions to
the optimal control problem were obtained using Nonlinear
Trajectory Generation (NTG) software. The resulting solution
is compared to corresponding results on LCS obtained using
the Direct Lyapunov Exponent method. The velocity data
used for these computations was obtained from measurements
taken in August, 2000, by HF-Radar stations located around
Monterey Bay, CA
A receding horizon generalization of pointwise min-norm controllers
Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved
A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations
In this paper, we develop regularized discrete least squares collocation and
finite volume methods for solving two-dimensional nonlinear time-dependent
partial differential equations on irregular domains. The solution is
approximated using tensor product cubic spline basis functions defined on a
background rectangular (interpolation) mesh, which leads to high spatial
accuracy and straightforward implementation, and establishes a solid base for
extending the computational framework to three-dimensional problems. A
semi-implicit time-stepping method is employed to transform the nonlinear
partial differential equation into a linear boundary value problem. A key
finding of our study is that the newly proposed mesh-free finite volume method
based on circular control volumes reduces to the collocation method as the
radius limits to zero. Both methods produce a large constrained least-squares
problem that must be solved at each time step in the advancement of the
solution. We have found that regularization yields a relatively
well-conditioned system that can be solved accurately using QR factorization.
An extensive numerical investigation is performed to illustrate the
effectiveness of the present methods, including the application of the new
method to a coupled system of time-fractional partial differential equations
having different fractional indices in different (irregularly shaped) regions
of the solution domain
Examination of accelerated first order methods for aircraft flight path optimization
Accelerated first order methods for aircraft flight path optimizatio
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