Stability Results for Simple Traffic Models Under PI-Regulator Control
Iasson Karafyllis, Markos Papageorgiou
TL;DR
This paper analyzes the stability of simple traffic models controlled by PI-regulators, providing conditions for global and local stability, and illustrating results with examples.
Contribution
It offers new necessary and sufficient conditions for stability of uncertain traffic models under PI control, including local stability region estimates.
Findings
Conditions for global input-to-state stability
Estimation of local stability regions via Lyapunov functions
Illustrative examples demonstrating theoretical results
Abstract
This paper provides necessary conditions and sufficient conditions for the (global) Input-to-State Stability property of simple uncertain vehicular-traffic network models under the effect of a PI-regulator. Local stability properties for vehicular-traffic networks under the effect of PI-regulator control are studied as well: the region of attraction of a locally exponentially stable equilibrium point is estimated by means of Lyapunov functions. All obtained results are illustrated by means of simple examples.
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