A CASE STUDY OF THE DISCRETE OPTIMUM FILTER-CONTROLLER PROBLEM.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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An example is given of the steps and calculations necessary to the synthesis of the discrete optimum controller and Kalman filter for the control of a linear, timeinvariant plant whose state is only partially observable. The plant is subject to random excitation, and the observables are contaminated by random measurement noise. The optimum control is a linear function of the best estimate of the system state variables. The controller gains are obtained from the steady-state solution of a set of recursion equations arising from a dynamic programming approach to the minimization of a quadratic index of performance. The optimum filter is essentially a model of the plant. The state of the model is the best current estimate of the state of the plant. The estimate is updated at each sampling instant by taking the difference between the observed state of the plant and the predicted state of the model. This difference vector is multiplied by a gain matri to adjust the model. The elements of the filter gain matrix are obtained from the steady-state solution of a set of recursion equations developed by Kalman.
- Operations Research
- Computer Hardware