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Center for Nonlinear Studies |
This talk examines a class of structured decentralized control problems for positive systems in which the control signal enters bilinearly with the state. Such dynamics arise, for example, when modeling the evolutionary dynamics of HIV in the presence of drug therapy and in the leader selection problem for directed consensus networks. First we establish convexity of the H_2 and H_infinity norms over constant control signals. In contrast to previous work on this problem, our formulation allows for arbitrary convex constraints and regularization of the control signal itself. Then, to explore the utility of time-varying control signals, we formulate an infinite horizon optimal control problem and show that the optimal control signal is constant over time. We further extend our results to the case of uncertain dynamics and provide a characterization of the optimal robust controller. Finally, we explore the drug therapy design and leader selection problems and provide connections with graph theory.
Host: Anatoly Zlotnik