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

TL;DR

This paper introduces fast Newton-type algorithms for solving constrained linear-quadratic dynamic games, enabling real-time autonomous vehicle control with demonstrated superior performance in traffic scenarios.

Contribution

It reformulates infinite-horizon Nash equilibria as receding-horizon affine variational inequalities and develops Newton methods with local quadratic convergence for efficient solutions.

Findings

Algorithms achieve extremely fast convergence suitable for real-time control.

Simulations show substantial performance gains over first-order methods.

Methods demonstrate high potential for safety-critical traffic applications.

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.