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.

中文翻译：

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利用双向不等式约束在异构车辆排的最优鲁棒控制中

这项研究研究了非线性和（可能是快速的）时变不确定性的异构车辆排的鲁棒控制问题。不确定性是由参数变化和外部干扰引起的。不确定性的界限通过连续函数来描述。首先，将排建模为耦合不确定动态系统。为了保证避免碰撞和紧凑的编队性能，对相邻车辆之间的间距误差建立了双向不等式约束。提出了一种数学变换方案，将有界状态转换为无界状态。然后，基于Udwdia–Kalaba方法和Lyapunov稳定性理论，设计了约束约束鲁棒控制器。控制器提供了无界状态的统一有界性和统一的最终有界性性能，从而又保证了对间距误差的双向限制。此外，提出了一种针对该控制器的可调参数的最佳设计方案，以最小化涉及系统性能和控制成本的综合指标。最后，通过数值模拟验证了所提算法的有效性。