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Filtering and stochastic control: a historical perspective

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1 Author(s)
S. K. Mitter ; Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA

We attempt to give a historical account of the main ideas leading to the development of nonlinear filtering and stochastic control as we know it today. We present a development of linear filtering theory, beginning with Wiener-Kolmogoroff filtering and ending with Kalman filtering. The linear-quadratic-Gaussian problem of stochastic control is considered and states that for this problem the optimal stochastic control can be constructed by solving separately a state estimation problem and a deterministic optimal control problem. Many of the ideas presented here generalize to the nonlinear situation. A reasonably detailed discussion of nonlinear filtering, again from the innovations viewpoint, is given. Finally, we deal with optimal stochastic control. The general method of discussing these problems is dynamic programming

Published in:

IEEE Control Systems  (Volume:16 ,  Issue: 3 )