Frequency Theorem for discrete time stochastic system with multiplicative noise

Details Frequency Theorem for discrete time stochastic system with multiplicative noise Frequency Theorem for discrete time stochastic system with multiplicative noise

2011-06-19

arxiv.org/abs/1106.3759v2

Mathematics

Optimization and Control

Scientific paper

In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and sufficient conditions for the existence of the optimal control can be formulated as matrix inequalities in frequency domain. Furthermore, we show that if the optimal control exists, then certain Lyapunov equations must have a solution. The optimal control is obtained by solving a deterministic linear-quadratic optimal control problem whose functional depends on the solution to the Lyapunov equations. Moreover, we show that under certain conditions, solvability of the Lyapunov equations is guaranteed. We also show that, if the frequency inequalities are strict, then the solution is unique up to equivalence.

Affiliated with

Also associated with

No associations

Rating

Frequency Theorem for discrete time stochastic system with multiplicative noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Frequency Theorem for discrete time stochastic system with multiplicative noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Frequency Theorem for discrete time stochastic system with multiplicative noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-723316