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

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)
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