1. M. Sadeghi, M.A. Al-Radhawi, M. Margaliot, and E.D. Sontag. No switching policy is optimal for a positive linear system with a bottleneck entrance. IEEE Control Systems Letters, 3:889-894, 2019. Note: (Also in Proc. 2019 IEEE Conf. Decision and Control.). [PDF] Keyword(s): entrainment, switched systems, RFM, ribosome flow model, traffic systems, nonlinear systems, nonlinear control. Abstract:

   We consider a nonlinear SISO system that is a cascade of a scalar "bottleneck entrance" with a stable positive linear system. In response to any periodic inflow, all solutions converge to a unique periodic solution with the same period. We study the problem of maximizing the averaged throughput via controlled switching. We compare two strategies: 1) switching between a high and low value, and 2 ~using a constant inflow equal to the prescribed mean value. We show that no possible switching policy can outperform a constant inflow rate, though it can approach it asymptotically. We describe several potential applications of this problem in traffic systems, ribosome flow models, and scheduling at security checks.

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