Optimal H2 / H∞ Consensus Based on Particle Swarm Optimization Method to Stability of Third-Order Self-Driving Car Platoons Under External Disturbance

In this article, the optimal robust H2 / H∞ control of self-driving car platoons (SDCPs) under external disturbance is investigated. By considering the engine dynamics and the effects of external disturbance, a linear dynamical model is presented to define the motion of each self-driving car (SDC). Each following SDC is in direct communication with the leader. By utilizing the relative position of following SDCs and the leader, the error dynamics of each SDC is calculated. The particle swarm optimization (PSO) method is utilized to find the optimal control gains. To this aim, a cost function which is a linear combination of H2 and H∞ norms of the transfer function between disturbance and target variables is constructed. By employing the PSO method, the cost function will be minimized and therefore, the robustness of the controller against external disturbance is guaranteed. It will be proved that under the presented robust control method, the negative effects of disturbance on system performance will significantly reduce. Therefore, the SDCP is internally stable and subsequently, each SDC tracks the motion of the leader. In order to validate the proposed method, simulation examples will be presented and analyzed.