Thomas Parisini

In this tutorial lecture we present some key use-cases of challenging optimisation problems - centralised and distributed - in which it is shown that a control theoretic approach can have a considerable impact, especially when robustness is considered. Methodologies and tools such as Lyapunov analysis, ISS stability, small-gain theory, time-scales separation, and passivity are all instrumental to unveil fundamental properties of optimisation methods with a significant potential impact on key application areas such as multi-agent systems and large-scale critical infrastructures.

In the first use-case, we consider the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm, also known as the first-order Lagrangian method, for constrained optimisation problems involving a smooth strongly convex cost and smooth convex constraints. We deal with the long-standing open problem of nonlocal asymptotic stability of such an algorithm. In particular, it is proved that an optimal equilibrium exists, it is unique, and it is semi-globally exponentially stable. We also show that, in the presence of constraints, global asymptotic stability cannot be established for the considered algorithm; hence, semi-global guarantees are the best achievable in general.

In the second use-case, we revisit the distributed version of the unconstrained Arrow-Hurwicz-Uzawa primal-dual algorithm, which was introduced in 2010 by J. Wang and N. Elia. Here, by means of a Lyapunov-based analysis, we prove global ISS of the algorithm relative to a closed invariant set composed of optimal equilibria and with respect to perturbations affecting the algorithm’s dynamics. In the absence of perturbations, this result implies linear convergence of the local estimates and Lyapunov stability of the optimal steady state. Moreover, we unveil fundamental connections with the well-known Gradient Tracking algorithm and with distributed integral control.

In the third use-case, as an extension of the Wang-Elia algorithm, we present a control approach to the problem of distributed optimisation for both continuous-time and discrete-time, linear uncertain multi-agent systems. Since all the agent dynamics is subject to parametric uncertainties and the gradient of the local objective function can only be measured through each agent’s output, the output agreement of multi-agents cannot be achieved by traditional distributed optimisation algorithms. Instead, we propose a simple internal-model-based tracking controller as a new module, integrated into the Wang-Elia algorithm to accomplish the output agreement with guaranteed exponential convergence.

Finally, early preliminary attempts to address the distributed version of the constrained discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm by a control theoretic approach are briefly sketched showing that passivity tools are instrumental in this challenging context.

Biography:

I received the ``Laurea'' degree (Cum Laude and printing honours) in Electronic Engineering from the University of Genoa in 1988 and the Ph.D. degree in Electronic Engineering and Computer Science in 1993. I was with Politecnico di Milano, and I hold the Chair of Industrial Control at Imperial College London. I'm serving as the Head of the Control and Power Research Group and I served as Director of Research at the Dept. of Electrical and Electronic Engineering. I'm also Professor and Danieli Endowed Chair of Automation Engineering with University of Trieste. In 2009-2012, I have been appointed Deputy Rector of University of Trieste. In 2018, I received an Honorary Doctorate from University of Aalborg, Denmark. I authored or co-authored a research monograph in the most prestigious series of Springer Nature and over 400 research papers in archival journals, book chapters, and international conference proceedings. My research interests include monitoring, diagnosis, control and security of large-scale critical infrastructure systems with applications in smart grids, transportation networks, power electronics and industrial process control. Among several awards, I was a co-recipient of the 2011-2013 IFAC Best Application Paper Prize of the Journal of Process Control, Elsevier, and of the 2004 Outstanding Paper Award of the IEEE Trans. on Neural Networks. I was also awarded the 2007 IEEE Distinguished Member Award. Among the major research grants, I was awarded as PI at Imperial the H2020 Flagship Teaming Project KIOS (total budget for the two partners over 40 MEuros). Moreover, I was awarded a prestigious ABB Research Grant and I was involved as Project Leader in several projects funded by the European Union and by the Italian Ministry for Research. Moreover, I secured several major grants from process control industries especially in the steel-making sector. I served as the 2021-2022 President of the IEEE Control Systems Society and during 2009-2016 I served as the Editor-in-Chief of the IEEE Trans. on Control Systems Technology. Since 2018 I am the Editor in Chief of the European Journal of Control. Since 2017, I'm also serving as Editor for Control Applications of Automatica. I served as the Chair of the IFAC Technical Committee on Fault Detection, Supervision & Safety of Technical Processes - SAFEPROCESS. I was the Chair of the IEEE Control Systems Society Conference Editorial Board and a Distinguished Lecturer of the IEEE Control Systems Society. I was an elected member of the Board of Governors of the IEEE Control Systems Society and of the European Control Association (EUCA) and a member of the board of evaluators of the 7th Framework and of the Horizon 2020 framework Research Program of the European Union. I'm also currently serving as an Associate Editor of the Int. J. of Control and I served as Associate Editor of the IEEE Trans. on Automatic Control, of the IEEE Trans. on Neural Networks. Among other activities, I was the Program Chair of the 2008 IEEE Conference on Decision and Control, the Program Chair of the 2018 European Control Conference, and General Co-Chair of the 2013 IEEE Conference on Decision and Control and of the 2018 IEEE Conference on Control Technology and Applications. I'm General Co-Chair of the 2022 European Control Conference. I am a Fellow of the IEEE and of IFAC.