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Keywords: optimal feedback, stochastic uncertainty, tracking error constraints, robust optimal control, stochastic optimization, computation of expectations, Taylor expansions.

Summary

A predetermined optimal feedback control should be "robust", i.e., the feedback law should guarantee satisfying results also in case of observational random errors and variations of the different stochastic parameters occurring in the model. In addition, for the tracking error several constraints have to be taken into account.

Based on the (optimal) reference trajectory and the related feedforward control, for the computation of a stochastic optimal feedback control, deterministic substitute control problems of the following type are considered: Minimize the expected total costs arising from the tracking error and the costs for the control correction, where the following constraints have to be taken into account: i) Dynamic equation of the stochastic control system with the total control input being the sum of the feedforward control and the control correction, ii) constraints "in the mean" and "almost sure" for the tracking error, iii) stochastic initial conditions, and iv) possible additional conditions for the feedback law.

The occurring expectations are determined approximatively by means of Taylor expansions with respect to the vector of parameter deviations and observation errors at zero means. The stochastic optimization problem for the feedback control law is converted then into a standard deterministic optimal control problem involving the gain matrices as the unknown matrix decision variables to be determined.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 108 PROCEEDINGS OF THE FIFTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping Paper 187 Optimal Feedback Control in case of Stochastic Uncertainty and Tracking Error Constraints K. Marti Aerospace Engineering and Technology Federal Armed Forces University Munich, Germany doi:10.4203/ccp.108.187 purchase the full-text of this paper Full Bibliographic Reference for this paper K. Marti, "Optimal Feedback Control in case of Stochastic Uncertainty and Tracking Error Constraints", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 187, 2015. doi:10.4203/ccp.108.187 Keywords: optimal feedback, stochastic uncertainty, tracking error constraints, robust optimal control, stochastic optimization, computation of expectations, Taylor expansions. Summary A predetermined optimal feedback control should be "robust", i.e., the feedback law should guarantee satisfying results also in case of observational random errors and variations of the different stochastic parameters occurring in the model. In addition, for the tracking error several constraints have to be taken into account. Based on the (optimal) reference trajectory and the related feedforward control, for the computation of a stochastic optimal feedback control, deterministic substitute control problems of the following type are considered: Minimize the expected total costs arising from the tracking error and the costs for the control correction, where the following constraints have to be taken into account: i) Dynamic equation of the stochastic control system with the total control input being the sum of the feedforward control and the control correction, ii) constraints "in the mean" and "almost sure" for the tracking error, iii) stochastic initial conditions, and iv) possible additional conditions for the feedback law. The occurring expectations are determined approximatively by means of Taylor expansions with respect to the vector of parameter deviations and observation errors at zero means. The stochastic optimization problem for the feedback control law is converted then into a standard deterministic optimal control problem involving the gain matrices as the unknown matrix decision variables to be determined. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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