Covariance Steering for Discrete-Time Linear-Quadratic Stochastic Dynamic Games [article]

Venkata Ramana Makkapati and Tanmay Rajpurohit and Kazuhide Okamoto and Panagiotis Tsiotras
2020 arXiv   pre-print
This paper addresses the problem of steering a discrete-time linear dynamical system from an initial Gaussian distribution to a final distribution in a game-theoretic setting. One of the two players strives to minimize a quadratic payoff, while at the same time tries to meet a given mean and covariance constraint at the final time-step. The other player maximizes the same payoff, but it is assumed to be indifferent to the terminal constraint. At first, the unconstrained version of the game is
more » ... amined, and the necessary conditions for the existence of a saddle point are obtained. We then show that obtaining a solution for the one-sided constrained dynamic game is not guaranteed, and subsequently the players' best responses are analyzed. Finally, we propose to numerically solve the problem of steering the distribution under adversarial scenarios using the Jacobi iteration method. The problem of guiding a missile during the endgame is chosen to analyze the proposed approach. A numerical simulation corresponding to the case where the terminal distribution is not achieved is also included, and discuss the necessary conditions to meet the terminal constraint.
arXiv:2003.03045v1 fatcat:lyrysnqz4badxj3apkkyds2q4m