Basic Optimal Estimation and Control Problems in Hilbert Space.
TEXAS TECH UNIV LUBBOCK INST FOR ELECTRONICS SCIENCE
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The recently developed mathematical framework of Hilbert resolution space valued random processes is used to formulate and solve an abstract quadratic optimization problem. By particularizing the description of the operators appearing in the statement and solution formula of this problem one rediscovers and generalizes most of the classical estimation and control theory problem statements and results. These results include, among others, the Wiener smoothing prediction filter, the Kalman regulator, the Kalman-Bucy filter, the stochastic control separation principle and the more recent Youla-Jabr-Bongiorno optimal servo problem solution. Author
- Statistics and Probability