Optimal Longitudinal Control for Vehicular Platoon Systems: Adaptiveness, Determinacy, and Fuzzy

This article addresses the control design problem for a fuzzy vehicular platoon system consisting of one leading vehicle and N following vehicles. Due to external disturbances, uncertainty exists in the platoon system and is usually nonlinear and possibly fast time varying. In order to deal with uncertainty, fuzzy theory is employed to describe the platoon system, thereby the so-called fuzzy vehicular platoon system. Based on the fuzzy property of uncertainty, a type of adaptive law is proposed. Since the original state of the system is one-side bounded when collision avoidance is taken into account, a state transformation is made, by which a new global state is obtained. Then, the swarm intelligence is embedded into the platoon system via a function, which mimics the swarm behavior. For the control design, we focus on adaptiveness and optimization. A switching-type adaptive robust control is proposed. The control is not IF-THEN rule based. We further explore the problem of control parameter optimization. A performance index consisting of transient control cost and average control cost is proposed. Aiming at minimizing the performance index, the optimal problem is formulated. The solution to the optimal problem (i.e., optimal control parameter) exists and is unique. The control with optimal parameter is called optimal control, which guarantees both deterministic performance (uniform boundedness, uniform ultimate boundedness, and collision avoidance) and fuzzy performance of the platoon system.