Finite-horizon optimal control with pointwise cost functional

摘要

A finite-horizon, discrete-time, optimal control problem is proposed and analyzed, where the uncertainty affecting the system is modeled as an input variable (disturbance) that at any time instant, is only known to belong to a given set. The functional to be minimized is the highest instantaneous cost that may occur under the worst possible combination of disturbances. A Dynamic Programming algoritm is proposed for the solution. Two simple but relevant examples of application (the target set reachability problem, and the control of a storage system) are presented.