Entropy for Optimal Control on a Simplex With an Application to Behavioral Nudging

We study the utilization of the entropy function of inputs in solving an Optimal Control Problem (OCP) with linear dynamics and inputs constrained to a variable-sized simplex in which the size is also an input. By using the entropy function as part of the objective functional in the OCP, we are able to derive a closed-form solution. Additionally, we present an example of how the studied OCP can be applied to choose between nudging techniques to discourage a specific behavior, such as non-adherence to medication, through the lens of behavioral momentum theory.