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2024-07-09 19:21| 来源: 网络整理| 查看: 265

HJB-solver

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

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

The most important functions 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. Arguments for the main function Argument Description Example t0 start of timehorizon 0 T end of timehorizon 1 N Number of time steps 10 M1, M2 Number of space steps 10 f0 affine part of the RHS @(t,x) x F linear part of the RHS @(t,x) sin(x) g Boundary value function @(t,x) t*exp(x) U Control set [1, 5] Omega0 initial set [2, 7]

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