The robust fault detection filter design for uncertain linear systems with nonlinear perturbations is formulated as a two-objective optimization problem. Solvable conditions for the existence of such a robust fault de...The robust fault detection filter design for uncertain linear systems with nonlinear perturbations is formulated as a two-objective optimization problem. Solvable conditions for the existence of such a robust fault detection filter are given in terms of matrix inequalities (MIs), which can be solved by applying iterative linear matrix inequality (ILMI) techniques. Particularly, compared with two existing LMI methods, the developed algorithm is more generalized and less conservative.An illustrative example is given to show the effectiveness of the proposed method.展开更多
The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the...The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the solution is given using the method of differential inequalities.展开更多
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By ...Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ the ratio of the nonlinear rate C to the tunneling coefficient V （i.e., r = O/V） determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.展开更多
In this paper, we apply the approach of conditional nonlinear optimal perturbation related to the parameter(CNOP-P)to study parameter uncertainties that lead to the stability(maintenance or degradation) of a grassland...In this paper, we apply the approach of conditional nonlinear optimal perturbation related to the parameter(CNOP-P)to study parameter uncertainties that lead to the stability(maintenance or degradation) of a grassland ecosystem. The maintenance of the grassland ecosystem refers to the unchanged or increased quantity of living biomass and wilted biomass in the ecosystem,and the degradation of the grassland ecosystem refers to the reduction in the quantity of living biomass and wilted biomass or its transformation into a desert ecosystem. Based on a theoretical five-variable grassland ecosystem model, 32 physical model parameters are selected for numerical experiments. Two types of parameter uncertainties could be obtained. The first type of parameter uncertainty is the linear combination of each parameter uncertainty that is computed using the CNOP-P method. The second type is the parameter uncertainty from multi-parameter optimization using the CNOP-P method. The results show that for the 32 model parameters, at a given optimization time and with greater parameter uncertainty, the patterns of the two types of parameter uncertainties are different. The different patterns represent physical processes of soil wetness. This implies that the variations in soil wetness(surface layer and root zone) are the primary reasons for uncertainty in the maintenance or degradation of grassland ecosystems, especially for the soil moisture of the surface layer. The above results show that the CNOP-P method is a useful tool for discussing the abovementioned problems.展开更多
基金Supported by National Natural Science Foundation of P. R. China (60374021 and 60274015)Natural Science Foundation of Shandong Province (Y2002G05)
文摘The robust fault detection filter design for uncertain linear systems with nonlinear perturbations is formulated as a two-objective optimization problem. Solvable conditions for the existence of such a robust fault detection filter are given in terms of matrix inequalities (MIs), which can be solved by applying iterative linear matrix inequality (ILMI) techniques. Particularly, compared with two existing LMI methods, the developed algorithm is more generalized and less conservative.An illustrative example is given to show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation(10471039)Supported by the Natural Science Foundation of Zhejiang Province(102009)
文摘The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the solution is given using the method of differential inequalities.
基金Supported by National Natural Science Foundation of China under Grant No. 61078011
文摘Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ the ratio of the nonlinear rate C to the tunneling coefficient V （i.e., r = O/V） determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.
基金supported by the Foundation for Young University Key Teacher by the Educational Department of Henan Province (Grant No. 2014GGJS-021)the National Natural Science Foundation of China (Grant Nos. 41375111, 41675104 & 41230420)
文摘In this paper, we apply the approach of conditional nonlinear optimal perturbation related to the parameter(CNOP-P)to study parameter uncertainties that lead to the stability(maintenance or degradation) of a grassland ecosystem. The maintenance of the grassland ecosystem refers to the unchanged or increased quantity of living biomass and wilted biomass in the ecosystem,and the degradation of the grassland ecosystem refers to the reduction in the quantity of living biomass and wilted biomass or its transformation into a desert ecosystem. Based on a theoretical five-variable grassland ecosystem model, 32 physical model parameters are selected for numerical experiments. Two types of parameter uncertainties could be obtained. The first type of parameter uncertainty is the linear combination of each parameter uncertainty that is computed using the CNOP-P method. The second type is the parameter uncertainty from multi-parameter optimization using the CNOP-P method. The results show that for the 32 model parameters, at a given optimization time and with greater parameter uncertainty, the patterns of the two types of parameter uncertainties are different. The different patterns represent physical processes of soil wetness. This implies that the variations in soil wetness(surface layer and root zone) are the primary reasons for uncertainty in the maintenance or degradation of grassland ecosystems, especially for the soil moisture of the surface layer. The above results show that the CNOP-P method is a useful tool for discussing the abovementioned problems.
