Utilising bidirectional inequality constraints in optimal robust control for heterogeneous vehicular platoons

This study investigates the robust control problem of a heterogeneous vehicular platoon subject to non-linear and (possibly fast) time-varying uncertainties. The uncertainties are induced by parameter variations and external disturbances. The bound of the uncertainty is described via a continuous function. Firstly, the platoon is modelled as a coupled uncertain dynamic system. To guarantee collision avoidance and compact formation performance, the bidirectional inequality constraints are established for the spacing error between adjacent vehicles. A mathematical transformation scheme is proposed to convert the bounded state into an unbounded one. Then, based on the Udwdia-Kalaba approach and Lyapunov stability theory, a constraint-following robust controller is designed. The controller renders the uniform boundedness and uniform ultimate boundedness performance of the unbounded state, which in turn guarantees the bidirectional restrictions for the spacing error. Moreover, an optimal design scheme for the tunable parameter of this controller is proposed to minimise a comprehensive index involving the system performance and control cost. Finally, numerical simulations are conducted to validate the efficiency of the proposed algorithm.