Optimal point-wise discrete control and controllers' allocation strategies for stochastic distributed systems

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Abstract
The design of point-wise discrete controllers for a class of stochastic distributed -parameter systems is considered. Assuming a fixed set of controllers' positions, the optimal feedback control is derived using a direct approach in which the infinite dimensional space is approximated using a set of orthonormal functions. The resulting optimal cost is minimized again w.r.t. this set of positions, using gradient techniques, to get the optimal locations for the controller. A one-dimensional diffusion process is used to demonstrate the algorithm.

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