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Stagewise Newton Method for Dynamic Game Control with Imperfect State Observation

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 risksensitive 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.
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https://hal.inria.fr/hal-03705557
Contributor : Justin Carpentier Connect in order to contact the contributor
Submitted on : Monday, June 27, 2022 - 10:44:05 AM
Last modification on : Monday, July 25, 2022 - 4:50:45 PM

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Armand Jordana, Bilal Hammoud, Justin Carpentier, Ludovic Righetti. Stagewise Newton Method for Dynamic Game Control with Imperfect State Observation. IEEE Control Systems Letters, IEEE, 2022, ⟨10.1109/LCSYS.2022.3184657⟩. ⟨hal-03705557⟩

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