2019
- ▪M. Sadeghi, M.A. Al-Radhawi, M. Margaliot, E.D. Sontag, "No switching policy is optimal for a positive linear system with a bottleneck entrance", IEEE Control Systems Letters, vol. 3, pp. 889-894, 2019. pdf(Also in Proc. 2019 IEEE Conf. Decision and Control.)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.