Abstract
Abstract This paper considers the optimal control of a class of diffusion processes. Specifically, given a system with plant modelled as a finite-power series in the state and control variables and given certain statistical properties of additive plant noise, the problem is to minimize the expected value of a performance index by selecting a feedback control having a prescribed form—a finite-power series in the state variables, the coefficients of which are time functions to be determined The systems considered possess conditional state density functions that satisfy the forward equation. Then assuming an exponential series solution of the forward equation, the original problem is transformed into one requiring the determination of time functions (the aforementioned coefficients) that minimize a performance index while satisfying, together with the coefficients of the exponential expansion, an infinite set of ordinary differential equations In this paper, plant and control non-linearities are treated and ...
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