Abstract |
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Continuous-time control is considered, together with the corresponding allocation algorithm. The synthesis of a pointwise controller is carried out using the direct method, where the control is expanded in terms of a finite number of coordinate functions taken from a complete set of orthonormal basis. Given a fixed structure for the controller, the optimal control is derived that minimizes an average quadratic cost functional. Then the structure of the controller is optimized by optimally allocating the controllers in the spatial domain such that the given cost is minimized. The allocation procedure is carried out using gradient techniques. A computational algorithm is given and illustrated by an example of optimal regulation of a diffusion process. |