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In this paper, adaptive control is presented for a platoon of vehicles in the presence of parameter uncertainties. A constant time headway policy is employed for a platoon stable control design based on feedback linearization. Using Lyapunov synthesis, the developed adaptive controller guarantees the boundedness of spacing errors in the platoon. The parameter estimates eventually converge to their true values and the platoon achieves the desired performance that the platoon stability properties are ensured. As a consequence, the resulting vehicle platoon can operate without requiring communication of lead vehicle information.