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N.M. de Boer
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Max-Min-Plus-Scaling Approach to Urban Railway Systems
Modelling, Analysis, and Control of Bidirectional Urban Railway Systems with Origin–Destination Passenger Flows in the MMPS Framework
This Master's thesis employs the Max-Min-Plus-Scaling (MMPS) mathematical framework to model, analyse, and control an Urban Railways System (URS) featuring a bidirectional line and origin-destination passenger flows. MMPS systems utilise max-plus, min-plus, and conventional algebraic operations, and provide a powerful modelling language for Discrete Event Systems (DES) such as transportation networks, computer networks, and manufacturing plants. A comprehensive overview of MMPS systems is provided, covering the mathematical foundations, existing analysis techniques, and control strategies.
The thesis then advances the existing theory on the periodicity of MMPS systems by introducing the Interconnected Max-Min-Plus-Scaling (I-MMPS) framework, which incorporates dependencies on states x(k-d), with d>1, extending beyond the single-step dependency assumed in standard MMPS systems. The ABCD canonical form is derived for I-MMPS systems, and the existing analysis and control frameworks are extended accordingly, establishing conditions for time-invariance, bounded-buffer stability, and solvability, as well as a fixed controller design methodology.
These theoretical contributions are then applied to improve the existing unidirectional URS model. A return trip is incorporated to achieve bidirectional operation and origin-destination passenger flows are introduced without appending states to the state vector, keeping the computational complexity of eigenvalue computation to a minimum. The resulting Bidirectional Origin-Destination Urban Railway System (BiOD-URS) is analysed through a case study, examining its eigenvalue structure, dynamic behaviour, and response to various disturbances. Finally, state feedback controllers are designed and applied to the BiOD-URS to improve nominal performance and disturbance rejection, including a growth rate assignment controller that drives the system to a uniform steady state.
Overall, this thesis advances MMPS system theory through the development of the I-MMPS framework, and demonstrates its practical applicability through a comprehensive modelling, analysis, and control study of a complex urban railway system. ...
The thesis then advances the existing theory on the periodicity of MMPS systems by introducing the Interconnected Max-Min-Plus-Scaling (I-MMPS) framework, which incorporates dependencies on states x(k-d), with d>1, extending beyond the single-step dependency assumed in standard MMPS systems. The ABCD canonical form is derived for I-MMPS systems, and the existing analysis and control frameworks are extended accordingly, establishing conditions for time-invariance, bounded-buffer stability, and solvability, as well as a fixed controller design methodology.
These theoretical contributions are then applied to improve the existing unidirectional URS model. A return trip is incorporated to achieve bidirectional operation and origin-destination passenger flows are introduced without appending states to the state vector, keeping the computational complexity of eigenvalue computation to a minimum. The resulting Bidirectional Origin-Destination Urban Railway System (BiOD-URS) is analysed through a case study, examining its eigenvalue structure, dynamic behaviour, and response to various disturbances. Finally, state feedback controllers are designed and applied to the BiOD-URS to improve nominal performance and disturbance rejection, including a growth rate assignment controller that drives the system to a uniform steady state.
Overall, this thesis advances MMPS system theory through the development of the I-MMPS framework, and demonstrates its practical applicability through a comprehensive modelling, analysis, and control study of a complex urban railway system. ...
This Master's thesis employs the Max-Min-Plus-Scaling (MMPS) mathematical framework to model, analyse, and control an Urban Railways System (URS) featuring a bidirectional line and origin-destination passenger flows. MMPS systems utilise max-plus, min-plus, and conventional algebraic operations, and provide a powerful modelling language for Discrete Event Systems (DES) such as transportation networks, computer networks, and manufacturing plants. A comprehensive overview of MMPS systems is provided, covering the mathematical foundations, existing analysis techniques, and control strategies.
The thesis then advances the existing theory on the periodicity of MMPS systems by introducing the Interconnected Max-Min-Plus-Scaling (I-MMPS) framework, which incorporates dependencies on states x(k-d), with d>1, extending beyond the single-step dependency assumed in standard MMPS systems. The ABCD canonical form is derived for I-MMPS systems, and the existing analysis and control frameworks are extended accordingly, establishing conditions for time-invariance, bounded-buffer stability, and solvability, as well as a fixed controller design methodology.
These theoretical contributions are then applied to improve the existing unidirectional URS model. A return trip is incorporated to achieve bidirectional operation and origin-destination passenger flows are introduced without appending states to the state vector, keeping the computational complexity of eigenvalue computation to a minimum. The resulting Bidirectional Origin-Destination Urban Railway System (BiOD-URS) is analysed through a case study, examining its eigenvalue structure, dynamic behaviour, and response to various disturbances. Finally, state feedback controllers are designed and applied to the BiOD-URS to improve nominal performance and disturbance rejection, including a growth rate assignment controller that drives the system to a uniform steady state.
Overall, this thesis advances MMPS system theory through the development of the I-MMPS framework, and demonstrates its practical applicability through a comprehensive modelling, analysis, and control study of a complex urban railway system.
The thesis then advances the existing theory on the periodicity of MMPS systems by introducing the Interconnected Max-Min-Plus-Scaling (I-MMPS) framework, which incorporates dependencies on states x(k-d), with d>1, extending beyond the single-step dependency assumed in standard MMPS systems. The ABCD canonical form is derived for I-MMPS systems, and the existing analysis and control frameworks are extended accordingly, establishing conditions for time-invariance, bounded-buffer stability, and solvability, as well as a fixed controller design methodology.
These theoretical contributions are then applied to improve the existing unidirectional URS model. A return trip is incorporated to achieve bidirectional operation and origin-destination passenger flows are introduced without appending states to the state vector, keeping the computational complexity of eigenvalue computation to a minimum. The resulting Bidirectional Origin-Destination Urban Railway System (BiOD-URS) is analysed through a case study, examining its eigenvalue structure, dynamic behaviour, and response to various disturbances. Finally, state feedback controllers are designed and applied to the BiOD-URS to improve nominal performance and disturbance rejection, including a growth rate assignment controller that drives the system to a uniform steady state.
Overall, this thesis advances MMPS system theory through the development of the I-MMPS framework, and demonstrates its practical applicability through a comprehensive modelling, analysis, and control study of a complex urban railway system.