Fast Newton methods for linear-quadratic dynamic games with application to autonomous vehicle platooning and intersection crossing

Abstract

We consider constrained linear-quadratic dynamic games arising in autonomous vehicle platooning, intersection crossing and other cooperative driving scenarios. Infinite-horizon Nash equilibria are reformulated as receding-horizon affine variational inequalities with special structure. Exploiting this formulation, we design Newton-type algorithms with local quadratic convergence. The resulting methods achieve extremely fast convergence, making them well suited for real-time and embedded receding-horizon control in safety-critical traffic applications. Simulations of platooning and intersection crossing demonstrate substantial performance gains over first-order and operator-splitting approaches, hence high application potential.