The traffic signal affects the life of virtually everyone every
day. The effectiveness of signal systems can reduce the incidence
of delays, stops, fuel consumption, emission of pollutants, and accidents.
The problems related to rapid growth in traffic
congestion call for more effective traffic signalization using robust
feedback control methodology.
Online traffic-responsive signalization is based on real-time traffic
conditions and selects cycle, split, phase, and offset for the intersection
according to detector data. A robust traffic feedback control begins with
assembling traffic demands, traffic facility supply, and feedback
control law for the existing traffic operating environment. This information
serves the input to the traffic control process
which in turn provides an output in terms of the desired performance
under varying conditions.
Traffic signalization belongs to a class of hybrid systems since the
differential equations model the continuous behavior of the traffic flow
dynamics and finite-state machines model the discrete state changes of
the controller. A complicating aspect, due to the state-space
constraint that queue lengths are necessarily nonnegative, is that
the continuous-time system dynamics is actually the
projection of a smooth system of ordinary differential equations. This
also leads to discontinuities in the boundary dynamics
of a sort common in queueing problems.
The project is concerned with the design of a feedback controller to
minimize accumulated queue lengths in the presence of unknown inflow disturbances
at an isolated intersection and a traffic network with some signalized
intersections. A dynamical system has finite L2-gain if it is
dissipative in some sense. Therefore, the Hinfinity-control
problem turns to designing a controller such that the resulting closed
loop system is dissipative, and correspondingly there exists a storage
function.
The major contributions of this thesis include 1) to propose state space
models for both isolated multi-phase intersections and a class of queueing
networks; 2) to formulate Hinfinity problems for the control
systems with persistent disturbances; 3) to present the projection dynamics
aspects of the problem to account for the constraints on the state variables;
4) formally to study this problem as a hybrid system; 5) to derive traffic-actuated
feedback control laws for the multi-phase intersections. Though we have
mathematically presented a robust feedback solution for the traffic signalization,
there still remains some distance before the physical implementation. A
robust adaptive control is an interesting research area for the future
traffic signalization.
