GregorDeCillia/HJB-solver: Numerical solution of Hamilton Jacobi Bellman equa...

HJB-solver

Numerical tool to solve linear Hamilton Jacobi Bellman Equations. I.e. an equation of the form

$\dot{v}(t,x)=\nabla_xv(t,x)(f_0(t,x)+F(t,x)u), \ v(T,x)=v_T(x)$

It is assumed that the space and the control space are one dimenional.

$f_0,F:\mathbb{R}\times \mathbb{R} \rightarrow \mathbb{R},\ U\subseteq \mathbb{R}$

Function	Description
`I=reachableset(x,U,h,Psi,f0Psi,FPsi,f0,F)`	calculates discrete reachable sets. Note that this function does not depend on `g`.
`[Xi,v]=HJB( t0,T,N,M1,M2,f0,F,g,U,Omega0)`	Main function: Returns a Matrix of node Values and the corresponding values of v.
`v=optimization(Xi,vXi,I,i,j)`	Performs one step assuming the reachable set `I` has already been calculated.