Existence of solutions of two generalized riccati operator equations and their representation

Abstract

The solutions of two generalized Riccati operator equations are discussed in terms of two critical parameter values, which are related to the application of optimal control under unknown disturbances. Explicit formulas for calculating these two critical parameters as well as the closedform solutions of these two generalized Riccati operator equations are given. The connection between these two parameters and a zero-sum differential game is also investigated.

Keywords:

• Riccati operator equations
• Evolution systems
• Differential games

1991 Mathematics Subject Classification:

• Primary 47G20
• 93C20
• Secondary 93C50

^*Correspondence address: Tel.: [phone]. Fax: [phone]. [email protected].

^*Correspondence address: Tel.: [phone]. Fax: [phone]. [email protected].

Notes

^*Correspondence address: Tel.: [phone]. Fax: [phone]. [email protected].