Type of Document Dissertation Author Yu, Tungsheng Author's Email Address tyu@dcn.att.com URN etd-02298-16746 Title On-line Traffic Signalization using Robust Feedback Control Degree PhD Department Mathematics Advisory Committee

Advisor Name Title Ball, Joseph A. Committee Chair Kachroo, Pushkin Committee Member Russell, David L. Committee Member Thomson, James E. Committee Member Wheeler, Robert L. Committee Member Keywords

- robust control
- dissipative system
- trafic signalization
- intersection
- hybrid system
- Hamilton-Jacobi inequality
- finite state machines
- queueing network
Date of Defense 1997-12-18 Availability unrestricted AbstractThe 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 L_{2}-gain if it is dissipative in some sense. Therefore, the H_{infinity}-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 H

_{infinity}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.Files

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