This paper addresses the control problem of heterogeneous vehicle platoons subject to disturbances and modeling errors. The objective is to guarantee spatialgeometry 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 H∞ 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. Index Terms-Vehicle platoon, integrated controller, tube-based model predictive control (TMPC), proportional multiple-integral (PMI) observer.

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In this paper, we aim to design the trajectory tracking controller for variable curvature duty-cycled rotation flexible needles with a tube-based model predictive control approach. A non-linear model is adopted according to the kinematic characteristics of the flexible needle and a bicycle method. The modeling error is assumed to be an unknown but bounded disturbance. The non-linear model is transformed to a discrete time form for the benefit of predictive controller design. From the application perspective, the flexible needle system states and control inputs are bounded within a robust invariant set when subject to disturbance. Then, the tube-based model predictive control is designed for the system with bounded state vector and inputs. Finally, the simulation experiments are carried out with tube-based model predictive control and proportional integral derivative controller based on the particle swarm optimisation method. The simulation results show that the tube-based model predictive control method is more robust and it leads to much smaller tracking errors in different scenarios.

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