Global solutions of a class of discrete-time backward nonlinear equations on ordered Banach spaces with applications to Riccati equations of stochastic control

作者：Ungureanu V M^*; Dragan V; Morozan T

来源：Optimal Control Applications and Methods, 2013, 34(2): 164-190.

DOI：10.1002/oca.2015

• discrete-time nonlinear equations
• Riccati equations
• stabilizability
• minimal solution
• maximal solution
• stabilizing solution
• strong detectability

In this paper, we consider the problem of existence of certain global solutions for general discrete-time backward nonlinear equations, defined on infinite dimensional ordered Banach spaces. This class of nonlinear equations includes as special cases many of the discrete-time Riccati equations arising both in deterministic and stochastic optimal control problems. On the basis of a linear matrix inequalities approach, we give necessary and sufficient conditions for the existence of maximal, stabilizing, and minimal solutions of the considered discrete-time backward nonlinear equations. As an application, we discuss the existence of stabilizing solutions for discrete-time Riccati equations of stochastic control and filtering on Hilbert spaces. The tools provided by this paper show that a wide class of nonlinear equations can be treated in a uniform manner.

• 出版日期2013-4