# Vincent Liu's talk on An Introduction to Max-Plus Algebra and its Application to Optimal Control Problems

**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.