Theory of Stochastic Optimal Tracking Systems.
CALIFORNIA UNIV IRVINE DEPT OF ELECTRICAL ENGINEERING
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The object is to study the optimal tracking of signals modeled as stochastic processes, by linear plants. The signal available to the plant is a given stochastic process in the presence of a white noise. The criterion for optimization is the minimization of the original stochastic process and the plant output. The study thus involves the design of appropriate compensators to give the systems the desired tracking properties. The present theory of stochastic optimal tracking, in the mean-square sense, only considers stationary systems. The main thrust of this work is to extend the existing theory to include nonstationary systems. Thus nonstationary stochastic processes, time-varying plants and sensors, and arbitrary initial times are admissible in this work. Moreover, due to the nonstationary nature of the systems, state-space techniques are exclusively used here. The systems in the open-loop as well as the closed-loop configurations are studied. For each case, the appropriate compensators are designed both in terms of their impulse response functions and in terms of their state-space realizations. Finally, the conditions for the stability of the resulting systems are derived.
- Statistics and Probability