Marcello Colombino

Neil K. Dhingra, Marcello Colombino, Mihailo R. Jovanović

We study a class of structured optimal control problems in which the main diagonal of the dynamic matrix is a linear function of the design variable. While such problems are in general challenging and nonconvex, for positive systems we prove convexity of the $H_2$ and $H_\infty$ optimal control formulations which allow for arbitrary convex constraints and regularization of the control input. Moreover, we establish differentiability of the $H_\infty$ norm when the graph associated with the dynamical generator is weakly connected and develop a customized algorithm for computing the optimal solution even in the absence of differentiability. We apply our results to the problems of leader selection in directed consensus networks and combination drug therapy for HIV treatment. In the context of leader selection, we address the combinatorial challenge by deriving upper and lower bounds on optimal performance. For combination drug therapy, we develop a customized subgradient method for efficient treatment of diseases whose mutation patterns are not connected.

Neil K. Dhingra, Marcello Colombino, Mihailo R. Jovanović et al.

We consider a class of monotone systems in which the control signal multiplies the state. Among other applications, such bilinear systems can be used to model the evolutionary dynamics of HIV in the presence of combination drug therapy. For this class of systems, we formulate an infinite horizon optimal control problem, prove that the optimal control signal is constant over time, and show that it can be computed by solving a finite-dimensional non-smooth convex optimization problem. We provide an explicit expression for the subdifferential set of the objective function and use a subgradient algorithm to design the optimal controller. We further extend our results to characterize the optimal robust controller for systems with uncertain dynamics and show that computing the robust controller is no harder than computing the nominal controller. We illustrate our results with an example motivated by combination drug therapy.

Sergio Grammatico, Francesca Parise, Marcello Colombino et al.

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected 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 and to the constrained mean field charging control problem for large populations of plug-in electric vehicles.