In this talk, we present some results on the optimal control of implicit sweeping processes such as characterization of nonsmooth Lyapunov pairs and parametric stability. Some applications to implicit evolution variational inequalities are given.
This talk is concerned with a state constrained optimal control problem governed by a perturbed Moreau's sweeping process. The focus of the talk is on the Bellman approach for an infinite horizon problem. In particular, we focus on the regularity of the value function and on the Hamilton-Jacobi-Bellman equation it satisfies. We discuss a uniqueness result and we make a comparison with standard state constrained optimal control problem to highlight a regularizing effect that the sweeping process induces on the value function.
joint work with Ismael Pena, Geraldo Nunes Silva
This article concerns a predictive control framework to support decision-making in the context of resources management in which sustainability is achieved by deconflicting short-term - usually profit-seeking - goals of multiple agents, and the goal of seeking the the collective equilibrium in the sense of preserving the required production efficiency level. This class of problems arise in a very large spectrum of contexts such as agriculture, oceanic biomass exploitation, manufacturing, and services systems. In each one of these contexts, the competition among the multiple decision-makers often entails that each one adopts control strategies maximizing his/her profit in the short term, and, as a consequence, a long term depletion of the ingredients required to sustain the production efficiency of the overall system. Given the usual complexity of any realistic scenario, we consider an abstract context clarifying the core mathematical issues of a bi-level control architecture that, under some reasonable general assumptions, generates control strategies ensuring the asymptotic convergence to a sustainable global equilibrium while ensuring the economic (and, thus, social) short term sustainability.