1 research outputs found
Covariance Steering for Discrete-Time Linear-Quadratic Stochastic Dynamic Games
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 examined, 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