 The associated Hamilton-Jacobi-Bellman (HJB) equation is expressed in the piecewise manner across different regions to take into account  constraints.
<meaning-changed>  The associated Hamilton-Jacobi-Bellman (HJB) equation is expressed in the piecewise manner across different regions to take into account  constraints.
 The associated Hamilton-Jacobi-Bellman (HJB) equation can be heuristically expressed in a piecewise manner across different regions to take into account constraints.