Distributed control of interconnected systems and its application in traffic control

Doctoral thesis, 2016

Over the past few decades, the need for mobility and road transportation has been significantly increased over the world. This turned as a dilemma in many metropolitan areas as traffic congestion costs energy and takes time of all individuals who live in big cities. The exigency for advanced solutions arose when constructing new roads and infrastructures lost its eligibility due to e.g. financial and environmental cost. It then challenges scientists and traffic engineers to elaborate more accurate traffic models and more powerful intelligent transportation systems. The content of this thesis can be separated in two parts. The first part of the thesis focuses on traffic modelling and precisely on suggesting a proper method for describing traffic anomalies like traffic incidents. By introducing two parameters named as incident parameters, the well-known METANET model has been parametrised to describe the effect of traffic anomalies. Simulation and real traffic data has been employed in validating the idea. As the size of the system grows, collecting traffic data, analysing them and making decision become challenging due to scalability. Hence, the concept of distributed control seems a promising direction for analysis and synthesis of interconnected systems like traffic systems. Hence, the second part which is the major part of this thesis as well, deals with the synthesis of discrete time interconnected systems. Such systems are composed of smaller units called subsystems or agents. We let the subsystems belong to the wide class of Linear Parameter Varying systems with the rational dependancy on parameters. For such systems, we aim at designing a distributed control with induced L2 norm minimization chosen as performance requirement. Two types of control strategies are suggested in this thesis {i) scheduled state-feedback control and {ii) scheduled dynamic output feedback control. In both cases, a copy of subsystems' parameters and interconnection structure is used to schedule the controllers. Moreover, we incorporate the saturation of the control input in the distributed control framework. For that, we introduce a special structure in the controller matrices and we enforce this special structure in the synthesis procedure as well.