Risk-Averse Learning and Control for Distributed Dynamical Systems with Partial Information

This project aims at risk quantification in and risk-averse control of complex dynamical systems in unknown and changing environments with special attention to problems arising in underwater robotics. We consider multi-dimensional dynamical stochastic systems, in which partial observations are distributed in time and space, and the exchange of information between the subsystems is subject to substantial time and size limitations. A team of robots operating in an uncertain dynamic environment is a system of this type. In addition to the incompleteness of information stemming from the partial autonomy of the subsystems, the environment may constitute another source of uncertain dynamics. This multidisciplinary research will involve new theoretical foundations of models of risk for complex partially observable dynamical systems, statistical learning, risk-averse optimization and control under uncertainty, and robotics. It will also involve development of numerical methods for the new models, as well as experimental testing of mobile robotic systems in laboratory and field environments where these limitations are prevalent. Special attention will be given to popularizing the proposed research and its impact in these applied fields. In particular, this will be achieved through advising of graduate and undergraduate students, including students from underrepresented groups, presentations at popular, international and local forums, and dissemination of the obtained results via scientific journal and book publications. Models of risk aim at capturing the impact of low-probability but high-impact events. Classical approaches to such events include chance constraints, expected utility functions, or rank-dependent utility functions (distortions). Modern models of risk aversion are based on coherent or convex measures of risk and stochastic order constraints, which allow an emphasis on the tails of the relevant probability distributions, or the shaping of these distributions in a desirable way. Most studies in this area focus either on the risk model itself, or on specific centralized control problems with complete information. When information about the state of a system and its environment is incomplete and distributed, risk evaluation and control have not been addressed. Each subsystem has only partial knowledge of the other subsystems' states, and only local information about the environment. Controlling the system must involve learning the environment and system's uncertain state, exchanging information between subsystems, and risk evaluation. We intend to propose a general methodology for dynamic risk allocation and distributed risk-averse control. Three sources of risk must be understood and properly addressed: the risk due to an uncertain environment, the risk associated with not knowing the full state of the system (due to information limitations), and the risk associated with uncertain future evolution of the system and its environment. We emphasize that risk pertains both to the integrity of the system as well as to its performance, i.e., completing the mission successfully. A team of mobile robots operating in an underwater environment faces all aforementioned challenges. Environmental processes, such as winds, waves and currents, perturb the robots. The extent of uncertainty in the robots' sensor observations also depends on environmental factors. Underwater robots are also constrained by the bandwidth with which they can communicate wirelessly, and the range at which they are visible to one another.