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A theory of state covariance assignment for discrete systems. (English) Zbl 0613.93066
The paper considers discrete-time stochastic control problems with upper bunds on the variances of system states as well as on system inputs. The set of admissible state covariances, which may be assigned by state feedback, and the set of feedback gains are characterized. An algorithm is presented, which chooses recursively an admissible gain minimizing the input variances. If a Kalman filter is used to estimate the states, the presented theory leads to robust approximations. All results are based on the steady-state-behaviour of the system.
Reviewer: J.Stein

93E20Optimal stochastic control (systems)
62J10Analysis of variance and covariance
93C55Discrete-time control systems
93C05Linear control systems
93D15Stabilization of systems by feedback
49K45Optimal stochastic control (optimality conditions)
93E25Computational methods in stochastic control
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