Title: An Introduction to Max-Plus Algebra and its Application to Optimal Control Problems
Time, Date, Location: 11:00, Friday, 13 January, 2023, Brian Anderson Building Seminar Room
Abstract: Control, estimation, and system identification of nonlinear systems continues to be a challenging problem owing to a lack of structure imposed by most problem settings. However, the growing availability of data and advancements in computing power has given rise to a resurgence of operator-theoretic approaches such as the Koopman framework, which has been realised in algorithms like the Extended Dynamic Mode Decomposition. Such approaches involve embedding a nonlinear, finite-dimensional system in an infinite-dimensional space of functions, whose time evolution can be described by a linear operator. Along similar lines, this tutorial-style talk will discuss how the evolution of the value function for a nonlinear optimal control problem can be approximated in a computationally efficient manner. In particular, the Dynamic Programming Principle, which relates the value function at two time points, is a linear operator in a max-plus semi-vector space of functions. This then allows the value function to be evolved as if it were a discrete-time linear system. The talk will be packaged in a way that is accessible with only a basic understanding of linear algebra.