Quadratic control problem for linear discrete-time time-varying systems with multiplicative noise in the Hilbert spaces. (English) Zbl 1097.93039

Ungureanu, Viorica Mariela

Math. Rep., Bucur. 7(57), No. 1, 73-89 (2005).

Summary: We prove that under stabilizability and uniform observability conditions the discretetime Riccati equation associated to the general quadratic control problem has a unique, uniformly positive, bounded on \(\mathbb N^*\) solution. We use this result to solve the problem of existence of an optimal control for the cost function investigated.

MSC:

93E20	Optimal stochastic control
49N10	Linear-quadratic optimal control problems
39A11	Stability of difference equations (MSC2000)

Keywords:

exponential stability; detectability and observability; quadratic control; Riccati equation