Necessary conditions for constant solutions of coupled Riccati equations in Nash games
The well-known theorem concerning open-loop linear-quadratic. Nash games states that under appropriate assumptions the corresponding open-loop controls can be constructed by explicit formulae, which contain the solution of coupled Riccati-type differential matrix equations (RDE). The purpose of the reviewed paper is to study the asymptotic behaviour of the mentioned matrix solution, as the time interval tends to infinity. For this purpose the corresponding obtained from RDE by replacing therein the derivatives by the zero matrices. Then conditions for the existence of solutions of ARE and assumptions under which the solution of (RDE) converges to the solution of (ARE) are derived. The estimate for the rate of convergence is obtained. Two examples illustrate the results.
coupled Riccati-type differential matrix equations
scientific article; zbMATH DE number 516809
scientific article