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A detailed system model for a vehicle travelling on an automated mainline guideway under a synchronous moving-cell control philosophy is proposed. The model takes account of position, velocity and acceleration errors as well as the dynamics of the vehicle's propulsion system and the effects of stochastic input disturbances. It is assumed that not all the vehicle's states will be available for measurement and, in addition, any measured states will be corrupted by noise. It is further assumed that a sampled-data control system is to be employed. The dynamic behaviour of the vehicle is initially described by a set of 1st-order, linear differential equations. The authors then develop the corresponding state-transition equation from which a state estimator and vehicle controller can be derived. The state estimator and controller are both optimal with respect to defined quadratic performance indices and, in addition, both are shown to be time-invariant and can be computed offline using simple recurrence relationships. The combined state-estimator and optimal-control law is shown to yield extremely good vehicle-response characteristics even with very noisy measurements and for large input disturbances.