Structured decentralized control of positive systems

Neil Dhingra, Univeristy of Minnesota

Abstract:  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 leader-follower networks and the evolutionary dynamics of HIV in the presence of combination drug therapy. We first establish convexity of the H2 and H∞ norms over the control signal itself. In contrast to previous approaches, this allows for arbitrary convex constraints and regularization of the control signal. We then consider 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. Finally, we apply our methodology to the combination drug therapy design problem for HIV.