Stagewise Newton Method for Dynamic Game Control with Imperfect State Observation

TL;DR

This paper introduces a low-complexity, iterative Newton-based method for dynamic game control under imperfect state observations, enabling risk-sensitive decision-making with guaranteed convergence.

Contribution

The paper presents a novel, efficient algorithm combining backward and forward recursions for local Nash equilibrium computation in imperfect information settings.

Findings

Algorithm has linear complexity in time horizon.

Guarantees convergence via merit function and line search.

Demonstrates risk-sensitive control in robotic simulations.

Abstract

In this letter, we study dynamic game optimal control with imperfect state observations and introduce an iterative method to find a local Nash equilibrium. The algorithm consists of an iterative procedure combining a backward recursion similar to minimax differential dynamic programming and a forward recursion resembling a risk-sensitive Kalman smoother. A coupling equation renders the resulting control dependent on the estimation. In the end, the algorithm is equivalent to a Newton step but has linear complexity in the time horizon length. Furthermore, a merit function and a line search procedure are introduced to guarantee convergence of the iterative scheme. The resulting controller reasons about uncertainty by planning for the worst case disturbances. Lastly, the low computational cost of the proposed algorithm makes it a promising method to do output-feedback model predictive control on complex systems at high frequency. Numerical simulations on realistic robotic problems illustrate the risk-sensitive behavior of the resulting controller.