Dynamic optimisation: systematic methods to construct (low complexity) approximate solutions  


In this talk we will consider two classes of dynamic optimisation problems, i.e. optimal control and differential games. The solution of such problems is characterised by nonlinear partial differential equations, which are challenging to solve in practice. We will consider two different approaches to systematically construct approximate solutions of dynamic optimisation problems, without requiring the solution of any partial differential equality. First, considering dynamic programming in the context of optimal control and differential games, we will see that it is possible to construct approximate solutions – with the level of approximation quantifiable (and, hence, minimisable) – based solely on immersion and algebraic conditions (in place of partial differential equations). Second, we will see that solutions of optimal control problems can be constructed by considering insights provided by dynamic programming and Pontryagin’s minimum principle simultaneously. Namely, exploiting properties of the Hamiltonian system associated with a given optimal control problem, approximate solutions can be characterised by (relatively simple) conditions involving trajectories of the Hamiltonian system. 


Thulasi Mylvaganam received the M.Eng degree in Electrical and Electronic Engineering from Imperial College London, UK, in 2010. She completed her Ph.D. degree in 2014 in the Department of Electrical and Electronic Engineering, Imperial College London, UK, where she was a Research Associate from 2014-2016. From 2016-2017 she was a Research Fellow in the Department of Aeronautics, Imperial College London, UK, where she is currently a Senior Lecturer (Associate Professor). Her research interests include nonlinear control, optimal control, game theory, distributed control and data-driven control. She is Associate Editor for the IEEE CSS Conference Editorial Board and member of the IFAC Technical Committee on Optimal Control. 


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