Learning control of failure avoidance problems with known analytical form of cost function

We study adaptive critic designs for a class of failure avoidance control problems. We categorize such problems by the choice of local cost function as zero throughout a trial except at the last time step when a failure occurs. We derive an analytical form of its overall cost function defined as the infinite summation of the local cost function over time. We demonstrate that the outputs of the critic network after learning resemble well the analytically derived cost function.