Seminar - Dejan Milutinović Mar. 14

Solving nonlinear control problems in the presence of uncertainty, or so-called stochastic control problems, that appear naturally in multi-agent systems and robotics can be enormously complex. This complexity is due to nonlinearities, many degrees of freedom and a large number of agents, as well as environmental uncertainties and noisy observations. The focus of this talk is on open-loop stochastic control problems, which are more general than their close-loop counterparts. When the state of a dynamical system is described by both discrete and continuous variables, i.e., by the hybrid state, the state probability density function obeys a system of partial differential equations. Consequently, we consider open-loop stochastic control problems as the problem of controlling state probability density function evolutions. Our approach is unique in that we address stochastic optimal control using an abstract Pontryagin-like minimum principle. We also show that by relying on stochastic process properties, computational methods defining the control variables can be greatly simplified. This talk will be illustrated with several examples, including aerial vehicle navigation and the control of a large size team of agents.