When it comes to modelling uncertain systems, there exist two prevailing approaches; namely, to determine (bounded) sets that contain all possible realisations of the uncertain disturbances or parameters, and to consider a certain probability distribution of the uncertainty. The former approach disregards any statistical or probabilistic information that is usually available and leads to overly conservative worst-case formulations, while the latter relies on the assumption that the underlying probability distributions are exactly known. In practice the characteristics of such uncertain disturbances are estimated from data, therefore one needs to take into account this uncertain uncertainty in order to design performant and reliable control and estimation systems.
Risk-averse model predictive control (MPC) is an optimisation-based control methodology that accounts for the inexact knowledge of the involved probability distributions using the theory of risk measures and unifies the worst-case and stochastic formulations of MPC. In fact, the risk-averse approach allows to interpolate between the worst-case (minimax) and expectation-based flavours of MPC and calls for new notions of (risk-based) stability that generalise robust and mean square stability. In light of the inexact knowledge of the probability distributions, probabilistic (aka chance) state constraints become what is known as ambiguous chance constraints and can be approximated by risk-based constraints. In multistage optimal control formulations, one needs to take into account the propagation of ambiguity in time which leads to multistage ambiguous chance constraints.
Risk-averse MPC problems can lead to exceptionally large-scale problems where the cost function is expressed as the composition of several non-smooth operators. However, risk-averse problems possess a certain structure that can be exploited to devise massively parallelisable (proximal) numerical optimisation algorithms that can run on graphics processing units (GPUs) and allow us to solve them fast and accurately.
About the speaker
Dr Pantelis Sopasakis was born in Athens, Greece, in 1985. He received a diploma (M.Eng.) in chemical engineering in 2007 and an M.Sc. with honours in applied mathematics in 2009 from the National Technical University of Athens.
In 2012, he defended his PhD thesis titled “Modelling and control of biological and physiological systems” at the School of Chemical Engineering, NTU Athens. He has held postdoctoral positions at IMT Lucca, KU Leuven and University of Cyprus. Since 2019 he has been a lecturer at the School of Electronics, Electrical Engineering and Computer Science (EEECS) and the i-AMS research centre at Queen’s University Belfast.
His current research interests revolve around model predictive control for uncertain systems and numerical optimisation methods and algorithms for large-scale stochastic optimal control problems