Systèmes différentiels et algébriques du type Riccati issus de la théorie des jeux

This work deals with differential and algebraic Riccati systems arising in linear quadratic differential games. These systems are concerned with Nash equilibrium and with optimal control under differential and stochastic constraint. These systems must be solved in order to obtain the optimal strategies for each player. For differential systems, we give an analytic form of the pair of solutions which can be obtained when we operate a changing of basis of the Nash matrix. In the case of algebraic systems, we have proposed the Lyapunov type iterations and the Riccati type iterations. Some properties of the iterative solutions and sufficent conditions for the convergence of the two iterations are established. Numerical results obtained with the two iterationq are presented and compared. These obtained results illustrate a better performance of the Riccati type iterations than the Lyapunov type ones.