Type: Seminar

Distribution: World

Expiry: 3 Sep 2014

CalTitle1: AGR Seminar: An introduction to umbral calculus with applications

Calendar2: 3 Sep 2014 1000-1100

CalLoc2: AGR Seminar

CalTitle2: AGR Seminar: An introduction to umbral calculus with applications

Auth: mathas@109.246.233.230 in SMS-auth

**Host venue**

University of Newcastle (CARMA)

**Abstract**

In this talk we consider economic Model Predictive Control (MPC) schemes. "Economic" means that the MPC stage cost models economic considerations (like maximal yield, minimal energy consumption...) rather than merely penalizing the distance to a pre-computed steady state or reference trajectory. In order to keep implementation and design simple, we consider schemes without terminal constraints and costs. In the first (longer) part of the talk, we summarize recent results on the performance and stability properties of such schemes for nonlinear discrete time systems. Particularly, we present conditions under which one can guarantee practical asymptotic stability of the optimal steady state as well as approximately optimal averaged and transient performance. Here, dissipativity of the underlying optimal control problems and the turnpike property are shown to play an important role (this part is based on joint work with Tobias Damm, Marleen Stieler and Karl Worthmann). In the second (shorter) part of the talk we present an application of an economic MPC scheme to a Smart Grid control problem (based on joint work with Philipp Braun, Christopher Kellett, Steven Weller and Karl Worthmann). While economic MPC shows good results for this control problem in numerical simulations, several aspects of this application are not covered by the available theory. This is explained in the last part of the talk, along with some suggestions on how to overcome this gap. Seminar 2

Classical umbral calculus was introduced by Blissard in the 1860's and later studied by E. T. Bell and Rota. It is a symbolic computation method that is particularly efficient for proving identities involving elementary special functions such as Bernoulli or Hermite polynomials. I will show the link between this technique and moment representation, and provide examples of its application.

**Seminar convenor**

Matthew Tam

**AGR technical support**

Andrew Danson

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If you would like to attend this seminar in our access grid room then please book the access grid room referring to this scnews item. Please liaise with the host institution to make any necessary arrangements and then send an email to accessgridroom@maths.usyd.edu.au to let the CSOs know of any special requirements for the seminar.