Coupled and generalized Riccati Equations

Abstract

The purpose of this chapter is to study coupled, non-symmetric and generalized Riccati equations occurring in different control problems. Three main topics are addressed: Dynamic games, linear systems with Markovian jumps and generalized Riccati equations appearing in stochastic control. In all these cases when quadratic criteria have to be minimized the control is expressed in terms of solutions of coupled or generalized Riccati equations. However, all these equations cannot be treated using the same approach. It will be shown that, depending on the nature of these equations, different methods could be employed to analyze and then to solve such Riccati equations.