Optimal Control with Stochastic Noise

**STOCHASTIC_GRADIENT_ND_NOISE**
is a MATLAB program which
solves an optimal control problem involving a functional over a system
with stochastic noise,
by Jeff Borggaard, Catalin Trenchea, Clayton Webster.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**STOCHASTIC_GRADIENT_ND_NOISE** is available in
a MATLAB version.

BLACK_SCHOLES, a MATLAB library which implements some simple approaches to the Black-Scholes option valuation theory;;

CNOISE, a MATLAB library which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov.

ONED, a MATLAB library which contains functions useful for 1D finite element calculations.

OPTIMAL_CONTROL_1D, a MATLAB program which seeks the optimal control function for a one dimensional system which is represented using the finite element formulation;

PCE_LEGENDRE, a MATLAB program which assembles the system matrix associated with a polynomal chaos expansion of a 2D stochastic PDE, using Legendre polynomials;

STOCHASTIC_DIFFUSION, MATLAB functions which implement several versions of a stochastic diffusivity coefficient.

Jeff Borggaard, Catalin Trenchea, Clayton Webster.

- exact_expected_value.m returns the exact expected value of the solution and the control.
- f_function.m RHS function from exact coefficient Q and the exact solution U.
- monte_carlo.m returns the physical coordinates of Monte Carlo abscissas.
- oned_bilinear.m integrates kernel(x) * basis function(x) * test function(x).
- oned_f_int.m computes the integral of f(x) times a test function.
- oned_gauss.m sets Gauss integration points on (-1,1).
- oned_mesh.m generates a mesh with a prescribed density. This routine returns elements of the same type as xb, e_connb (linear or quadratic)
- oned_shape.m computes test functions and derivatives for a Lagrange C0 element given element coordinates and Gauss points. (assumes all nodes are uniformly distributed in the element.)
- optimal_control.m is a script to solve the optimal control problem.
- q_exact.m evaluates the exact control coefficient function.
- u_hat.m is the exact target function to be matched.

- optimal_control_adjoint_mc_driver.m driver for the 1D optimal control problem.
- optimal_control_adjoint_mc_driver_output.txt the output file.
- figure01.png output figure 1.
- figure02.png output figure 2.
- figure05.png output figure 5.
- figure06.png output figure 6.
- figure07.png output figure 7.
- figure08.png output figure 8.

You can go up one level to the MATLAB source codes.