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Marcello Colombino

Marcello Colombino
Dr. sc. ETH Zürich, Postdoc

Automatic Control Laboratory
Swiss Federal Institute of Technology
Physikstrasse 3, ETL K 26

Phone: +41 44 632 4923

I recently joined the group of Prof. Florian Dörfler to work on on the European Project Migrate, studying the effect of massive integration of power electronic devices into the grid. I will research new control strategies for power inverters in order to guarantee the stability and performance of the power grid without rotational inertia.

I earned my Ph.D. in the Automatic Control Laboratory of ETH Zurich, Switzerland, under the supervision of Prof. Roy S. Smith and my MEng in Biomedical Engineering from Imperial College London.

Selected publications

For a complete list of my publications, see my Google Scholar page
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Robust and decentralized control of Positive Systems

During my PhD [C16] I focused mainly on the study of robust and decentralized control for positive systems. Positive systems arise in multiple application fields where the state variables are inherently nonnegative. In [CS16] we study the problem of assessing the robust stability of uncertain positive systems. We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems which are a strict superclass of positive systems. In particular, we show that the structured singular value is always equal to its convex upper bound for nonnegative matrices and we use this result to derive necessary and sufficient Linear Matrix Inequality (LMI) conditions for robust stability that involve only the system's static gain.

In [DCJ16] we study a class of structured optimal control problems for positive systems in which the design variable modifies the main diagonal of the dynamic matrix. For this class of systems, we establish convexity of both the H-2 and H-infinity optimal control formulations. In contrast to previous approaches, our formulation allows for arbitrary convex constraints and regularization of the design parameter. We provide expressions for the gradient and subgradient of the H-2 and H-infinity norms and establish graph-theoretic conditions under which the H-infinity norm is continuously differentiable. Finally, we develop a customized proximal algorithm for computing the solution to the regularized optimal control problems and apply our results for HIV combination drug therapy design.

[C16] Colombino, M.
Robust and Decentralized Control of Positive Systems: a Convex Approach.
ETH Zurich, 2016. [doi: 10.3929/ethz-a-010736004]
[CS16] Colombino, M. & Smith, R.S.
A Convex Characterization of Robust Stability for Positive and Positively Dominated Linear Systems.
Automatic Control, IEEE Transactions on, 61(7):1965-1971, 2016. [doi: 10.1109/TAC.2015.2480549]
[DCJ16] Dhingra, N.K., Colombino, M. & Jovanovic, M.
On the Convexity of a Class of Structured Optimal Control Problems for Positive Systems.
In Proceedings of the 2016 European Control Conference, 2016.

Structured Dynamic Games

In [CSS16] we formulate a two-team linear quadratic stochastic dynamic game featuring two opposing teams each with decentralized information structures. We introduce the concept of mutual quadratic invariance (MQI), which, analogously to quadratic invariance in (single team) decentralized control, defines a class of interacting information structures for the two teams under which optimal linear feedback control strategies are easy to compute. We show that, for zero-sum two-team dynamic games, structured state feedback Nash (saddle-point) equilibrium strategies can be computed from equivalent structured disturbance feedforward saddle point equilibrium strategies. However, for nonzero-sum games we show via a counterexample that a similar equivalence fails to hold. The results are illustrated with a simple yet rich numerical example that illustrates the importance of the information structure for dynamic games.

[CSS16] Colombino, M., Smith, R.S. & Summers, T.H.
Mutually Quadratically Invariant Information Structures in Two-Team Stochastic Dynamic Games.
Submitted To: Automatic Control, IEEE Transactions on, arXiv preprint arXiv:1607.05426, 2016.

Aggregative Games/Mean Field Control

In [GPC+16] we consider decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem.

[GPC+16] Grammatico, S., Parise, F., Colombino, M. & Lygeros, J.
Decentralized convergence to Nash equilibria in constrained mean field control.
Automatic Control, IEEE Transactions on, 2016.


For the material of the Game Theory and Control course, refer to the official course page. For the other classes I am involved in, please check lectures.

Master Thesis and Semester projects

Open projects