Presentation on YouTube.

In several engineering applications, it is desired to bring a system from an initial configuration to a specific terminal configuration. A motivational example is the multi-stage landing of reusable rockets which are required to come to full stop at an exact location on the landing platform in an upright configuration with all linear and angular velocities coming to zero. While in a deterministic setting, one can study these problems and provide theoretical guarantees for the satisfaction of the terminal state requirements, e.g., by employing the Minimum Principle (MP) and the Hybrid MP (HMP), no such guarantees can be provided for exact satisfaction of terminal state constraints in a stochastic setting and, inevitably, one needs to seek alternative expressions of the desired requirements and establish guarantees for those alternatives.

In this talk I will present two novel approaches, each with an alternative expression of the terminal state requirement within the stochastic systems framework, and each providing theoretical guarantees for optimality and the satisfaction of the associated terminal state constraints. The first approach is based on the Terminally Constrained Stochastic Minimum Principle (TCSMP) for the satisfaction of a family of constraints on the family of conditional expectations of the terminal state. The second approach is to impose constraints on the probability distribution of the terminal state and to derive the optimal inputs via a family of Hamilton-Jacobi (HJ) type equations established from the duality relationship between the space of measures and that of continuous functions. Numerical examples are provided to illustrate the results.

Bio: Ali Pakniyat is an Assistant Professor in the department of Mechanical Engineering at the University of Alabama. He received the B.Sc. degree in Mechanical Engineering from Shiraz University, the M.Sc. degree in Mechanical Engineering from Sharif University of Technology, and the Ph.D. degree in Electrical Engineering from McGill University. After holding two postdoctoral positions in the department of Mechanical Engineering at the University of Michigan and the Institute for Robotics and Intelligent Machines at Georgia Tech, he joined the University of Alabama in 2021 where he is now an Assistant Professor in the department of Mechanical Engineering.