This talk will fucus on some recent results about HJB approach to solve optimal control problems of Mayer's type with free initial state. First, wi show that such problems can be solved by using the associated value function as function of the initial state. Then, some sensitivity relations can be established to link the subdifferential of the value function and the adjoint state of the problem, coming from the Pontryagin's maximum principle. These theoretic results will be illustrated by practical examples from optimal control of bio-processes.
We study the control of a communicable disease in a prison. Its time evolution is modeled by a SIS model, typically used for illnesses that do not confer immunity after recovery. To control the disease, we consider an strategy that consists on performing a screening to a proportion (control variable) of the new prisoners, followed by a treatment. We determine the optimal strategies that minimize a tradeoff between the treatment cost and the number of infective prisoners, in a predetermined time horizon, and characterize qualitatively different behaviors depending on the model parameters
The maximin criterion, as the highest performance that can be sustained over time, promotes intergenerational equity, a pivotal issue for sustainability. The viable control approach, by investigating trajectories and actions complying over time with various standards and constraints, provides major insights into strong sustainability. In this presentation we address the links between maximin and viability approaches in a multi-criteria context, showing practical methods for computing sustainability standards based in dynamic programming principle and level-set approach.