Stochastic Optimal Control – Overview and Recent Advances

ABSTRACT: Stochastic optimal control lies within the foundation of mathematical control theory ever since its inception. Its usefulness has been proven in a plethora of engineering applications, such as autonomous systems, robotics, neuroscience, and financial engineering, among others. Specifically, in robotics and autonomous systems, stochastic control has become one of the most successful approaches for planning and learning, as demonstrated by its effectiveness in many applications, such as control of ground and aerial vehicles, articulated mechanisms and manipulators, and humanoid robots. In computational neuroscience and human motor control, stochastic optimal control theory has been used in the process of modeling the underlying computational principles of the neural control of movement. Furthermore, in financial engineering, stochastic optimal control provides the main computational and analytical framework, with widespread application in portfolio management and stock market trading.

The aim of this talk is to provide an overview on model-based stochastic optimal control and highlight some recent advances in its field. We will briefly present some well-established methods (Differential Dynamic Programming, Path Integral Control), illustrating their differences in approach and restrictive conditions. Motivated by these restrictive conditions, we will then present a novel framework for stochastic optimal control that capitalizes on the innate relationship between certain nonlinear PDEs and Forward and Backward Stochastic Differential Equations (FBSDEs), that relaxes some of these conditions. The utility of the proposed method will be demonstrated on some examples of L2- and L1- optimal control, as well as differential games.

BIO: Ioannis Exarchos received his Diploma degree (graduating valedictorian) in Mechanical Engineering and Aeronautics from the University of Patras, Greece, in 2010. He also received an M.S. degree in Mathematics in 2015, as well as his M.S. and Ph.D. degrees in Aerospace Engineering in 2013 and 2017 respectively, all from the Georgia Institute of Technology. During his PhD studies, he was an Onassis Foundation fellowship scholar. His research interests include stochastic optimal control, machine learning applications in control and neuroscience, dynamical systems and system identification, as well as differential game theory. He is currently a postdoctoral fellow at the Department of Biomedical Informatics, Emory University.

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