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| Author: | Fruchter, G.E. |
| Title: | A dual control problem and application to marketing |
| Journal: | European Journal of Operational Research
2001 : APR, VOL. 130:1, p. 99-110 |
| Index terms: | Control Estimation Marketing Promotion |
| Language: | eng |
| Abstract: | In the paper, an alternative deterministic approach is presented based upon determining a control in which a disturbance attenuation function remains bounded for all allowable (L2 functions) disturbances. The disturbance attenuation function is composed of the ratio of an L2 function of the desired outputs over an L2 function of the disturbance inputs. This disturbance attenuation problem is converted to a differential game. For this game, the optimal control law, in a closed-form, is obtained by performing a minmax operation with respect to a quadratic cost function subjected to a bi-linear system. The resulting controller is time-varying and depends non-linearly on the state and the parameter estimates vector, and on an associated Riccati-type matrix. Insights are provided into the structure of the resulting dual controller and illustrate the method by two examples. One of the examples is an application to marketing, to set promotional spending of a company, considering that the effect of promotional effort on sales is unknown. |
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