Filtering and Stochastic Control: A Historical Perspective
نویسنده
چکیده
In this paper we attempt to give a historical account of the main ideas leading to the development of non-linear filtering and stochastic control as we know it today. The paper contains six sections. In Section 2 we present a development of linear filtering theory, beginning with Wiener-Kolmogoroff filtering and ending with Kalman filtering. The method of development is the innovations method as originally proposed by Bode and Shannon and later presented in its modern form by Kailath. Section 3 is concerned with the Linear-Quadratic-Gaussian problem of stochastic control. Here we give a discussion of the separation theorem which 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 'This research has been supported by the Army Research Office under grant number DAAL 03-92-G-0115 (Center for Intelligent Control Systems).
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