  Path integral control solves a class of stochastic optimal control problems
with a Monte Carlo (MC) method for an associated Hamilton-Jacobi-Bellman (HJB)
equation. The MC approach avoids the need for a global grid of the domain of
the HJB equation and, therefore, path integral control is in principle
applicable to control problems of moderate to large dimension. The class of
problems path integral control can solve, however, is defined by requirements
on the cost function, the noise covariance matrix and the control input matrix.
We relax the requirements on the cost function by introducing a new state that
represents an augmented running cost. In our new formulation the cost function
can contain stochastic integral terms and linear control costs, which are
important in applications in engineering, economics and finance. We find an
efficient numerical implementation of our grid-free MC approach and demonstrate
its performance and usefulness in examples from hierarchical electric load
management. The dimension of one of our examples is large enough to make
classical grid-based HJB solvers impractical.
