This paper examines the role of random feedforward inputs in a probabilistic framework for stochastic control design in a discrete-time case. Fundamental rules of probability are applied to extend the Chapman—Kolmogorov equation by including the effect of the additional random disturbance variables. The steady state solution to this equation is then applied to the design of two long-term regulatory controllers: a probability-density-shaping controller and an approximation of an optimal controller with respect to a non-symmetric and non-quadratic cost functions.
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