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Dynamic model identification and state variables estimation from the corrupted measurement data have been attracted much research efforts during the recent years. In this way, Kalman and H-infinity filters have been increasingly used to estimate the parameters individually. In this paper, a mixed kalman-H_∞ filter is designed in an innovative approach using a multi-objective optimization method. It is desired to simultaneously employ the advantages of both filters to minimize both the root-mean squared errors and the upper bounds limit of estimation errors associated with Kalman and H-infinity filters, respectively. Some Pareto optimum design points are presented for two case studies from which trade-off optimum design points can be simply selected.

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The design of complex mechanical systems usually involves multiple mutually coupled disciplines and competing objectives which requires complicated and time-consuming interactive analysis during the design process. Multidisciplinary design optimization (MDO) is a systematic design methodology to improve the design efficiency of complex mechanical systems specifically in non-cooperative design environments. In the other hand game theory is set of mathematical constructs that study the interaction between multiple intelligent rational decision makers. In this paper, a new game theoretic approach is proposed and applied for multi-objective MDO problems in non-cooperative design environments, considering the intrinsic similarity between the MDO and game theory. In this way, genetic programming is used as a surrogate to construct the approximate rational reaction sets (RRS) of players. Furthermore, in order to find the intersection of RRS of players in Nash game models, an objective function is proposed which should be minimized. The effectiveness of the proposed framework is demonstrated by the design of three cases study in the field of engineering design optimization in non-cooperative environment. The results show that the presented approach is able to approximate complicated RRS, in addition has the ability to find multiple Nash solutions when the Nash solution is not a singleton and generally found solutions better than those reported in the literature.