Topics in Control. 2. Constrained Feedback Control of Linear Dynamic-Stochastic Systems.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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The design of feedback controllers which minimize some quadratic function of the outputs and inputs usually minimum mean square error at the output subject to constraints on the variances of the inputs is treated from two points of view Using discrete transfer function and ARIMA models to characterize the system and designing the optimal controllers by solving a discrete version of the Wiener-Hopf equation Using state variable models to characterize the system and solving the optimal control problem by employing dynamic programming and Kalman filtering. The two methods are shown to be equivalent and which is to be used is solely a matter of convenience. The relative merits of each is discussed and examples are given. Using the first approach a general form for constrained controllers is worked out. For the second approach the dynamic programming solution to the optimal control problem is given and a simplified solution is developed for the univariate unconstrained control case. Expressions for the covaraince matrices of the output and input under feedback control are derived. Different ways of dealing with time delays in the process dynamics are discussed. Author Modified Abstract
- Statistics and Probability