Stagewise Newton Method for Dynamic Game Control with Imperfect State Observation

Armand Jordana, Bilal Hammoud, Justin Carpentier, Ludovic Righetti

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)3241-3246
Number of pages6
JournalIEEE Control Systems Letters
StatePublished - 2022


  • Game theory
  • optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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