Dynamical Modeling and Predictive Control of Bus Transport Systems: A Hybrid Systems Approach

Bus operations, due to their unstable nature, are inefficient when left uncontrolled with respect to retaining headways. Irregularities such as bus bunching lead to loss of time and decrease bus service quality. Development of bus transport system management schemes to avoid bus bunching and improve performance are of high importance, and has thus been the focus of many works in the public transport systems literature. Motivated by the importance of developing bus control strategies for improving performance, and specifically by the lack of a detailed but computationally efficient mathematical model describing bus transport system dynamics in the literature (which can facilitate model-based control design), we propose a mixed logical dynamical model of a single loop bus transport system, which involves both continuous (e.g., bus positions) and binary (e.g., the state of a bus regarding whether it is holding at a certain stop or not) states. Furthermore, we develop a hybrid model predictive control scheme with actuation via bus speeds, which can regularize headways and improve bus service quality. Performance of the predictive controller is evaluated via simulation experiments using the proposed model, where the passenger demands and maximum bus speeds are extracted from data collected from the bus network of the city of Fribourg. Results indicate the potential of the proposed controller in avoiding bus bunching and decreasing passenger travel times.