This paper addresses the control problem of heterogeneous vehicle platoons subject to disturbances and modeling errors. The objective is to guarantee spatial-geometry constraints of vehicles in a platoon. We deal with the case where a predecessor-leader following (PLF) communication topology is used and heterogeneous vehicle dynamics is subject to disturbances. To estimate the lumped disturbance, the technique of unknown input proportional multiple-integral (PMI) observer is employed such that both the state and the disturbance are simultaneously estimated. Moreover, tube-based model predictive control (TMPC) is used and the corresponding control law is composed of a feed-forward term, a feedback term, and a disturbance compensation term. The gains in the integrated control strategy are optimized by utilizing the particle swarm optimization (PSO) algorithm with an mathscr H_{infty } performance index of an augmented error system. It is proved that the deviations between the actual system and the nominal system are bounded in a robustly positively invariant (RPI) set, that is, the main objective is guaranteed. With the proposed control strategy, simulations and comparisons are carried out. We can see that the control performance of the proposed strategy is significantly improved while the computational time is reduced compared with existing methods.