A Sparse Pinning Control for Vehicle Platoon via Sequential $\ell^{1}$ Optimization

This paper proposes a sparse pinning control method for vehicle platoon control. Our method controls a vehicle platoon by controlling some vehicles called pinning agents. The pinning agents and control inputs are optimized to reach a target velocity and a target inter-vehicular distance. We formulate this optimization problem as sequential $\ell^{1}$ sparse optimization and the input mapping. The input mapping ranks the elements from the optimized input vector in order of the size of the $\ell^{1}$ norm and sets all elements smaller than the specified ranking to 0. This ranking constraint expresses a constraint of the number of pinning agents. The calculation loads of our optimization method with the constraint of the number of pinning agents are smaller than other node selection problems and $\ell^{0}$ sparse optimization. The main concern of the sequential $\ell^{1}$ optimization is to reduce the computational load, and the sub concern is to attenuate the String-Instability.