Reverse Engineering Combination Therapies for Evolutionary Dynamics of Disease: An Hinfty Approach

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Vanessa Jonsson, Nikolai Matni and Richard M. Murray
2013 Conference on Decison and Control (CDC)

We propose a general algorithm for the systematic design of feedback strategies to stabilize the evolutionary dynamics of a generic disease model using an H1 approach. We show that designing antibody concentrations can be cast as an H1 state feedback synthesis problem, where the feedback gain is constrained to not only be strictly diagonal, but also that its diagonal elements satisfy an overdetermined set of linear equations. Leveraging recent results in positive systems, we additionally show that our algorithm always converges to a stabilizing controller.