Research Of Nonlinear Filtering And Control Theories And Its Application Based On Minimum Model Error Criterion

Nonlinear phenomenon has widespread existed in the aerospace field, especially for the complex spacecraft in the presence of serious uncertain model errors, which introduces the proegumenal cause to influence the accurancy and reliability of spacecraft system. Therefore, it is of significant to focuse on the research of nonlinear space system with uncertain model errors. Based on the theoretical mainline of “Minimum Model Error Criterion”, this thesis has investigated two basic theoretical problems involved in the nonlinear space system: State Estimation and Control. The first part has proposed some exploratory theoretical researches on the state estimation(filtering technology).Firstly, the theoretical shortcomings of the traditional predictive filter(PF) have been discussed with the further development on the basis of Sigma-Point theory. The PF is a kind of real-time nonlinear filter proposed on the basis of “Minimum Model Error Criterion”. The theoretical expand research on the traditional PF theory has been developed by using Sigma-Point sampling strategy, result in the presence of the unscented predictive filter(UPF), cubature predictive filter(CPF) and central difference predictive filter(CDPF) respectively. It is shown that these proposed filters can be described by using a unified framework; therefore, such filters are collectively named as Sigma-Point predictive filter(SPPF). It is verified that the proposed SPPF can capture the model error, posterior mean and covariance accurately to 2nd order for any nonlinear system. It is clear that the SPPF will have better filtering performance over the traditional PF, which is verified by the numerical simulation of attitude determination of spacecraft based on star sensors.Secondly, the practical applicability and stochastic stability of the proposed SPPF have been analyzed with theoretical details. With the advantages of Sigma-Point sampling strategy to expand the PF, the proposed SPPF can satisfy the condition of “Covariance Constraint” with higher precision over than the traditional PF. As a result, the dependence of SPPF on the model error weighting matrix will be reduced, which indicates the greater choice and more engineering practicality. In particular, the stochastic stability of SPPF has been analyzed and concluded that the estimation error remains stable and bounded if the system’s initial estimation error, disturbing noises as well as the model error are small enough and bounded. All the theoretical analyses have been demonstrated by the attitude determination of spacecraft.Thirdly, a novel predictive structure variable filter(PSVF) is presented with sufficient analysis and proofs. Based on the extension of the concept of “Minimum Model Error Criterion”, the “Generalized Minimum Model Error Criterion” is abstracted, which is the theoretical basis of the proposed PVSF. The new filter needs not to satisfy the constraint of Guassian random variable, and also get rid of the dependence on the weighting matrix. As the result of adopting sliding mode control strategy, the PVSF is endowed with low calculation burden without the covariance propagation. The relative position and attitude estimation of satellite formation is used to simulate that the PVSF is an ideal nonlinear filter with the significant advantages, such as the better robustness, more stable accuracy and.Finally, the adaptive investigation of the proposed PVSF is discussed with details. The choice of boundary layer of PVSF has been in-depth investigated. Hence, the adaptive predictive variable structure filter(APVSF) is developed by drawing the adaptive strategy. However, the loss of robustness for the APVSF occurs inevitably; thus, the corresponding solving strategies and expand researches has also been presented with details. It is shown that the Sigma-Point sampling strategy and orthogonality principle can significantly enchance the robustness of APVSF, which is verified by the simulation of attitude synchronization of distributed satellite formation.The second part focuses on the control theory of nonlinear space system with the uncertain model errors.The “Minimum Model Error Criterion” is mapped to the sliding mode control theory and abstracts the “Minimum Sliding Mode Error Criterion”, on which basis, a new kind of sliding mode control strategy is proposed with the name of minimum sliding mode error feedback control(MSMEFC). For the proposed controller, the actual sliding mode after MSMEFC will approximate to the ideal sliding mode in order to advance the control performance. In addition, the stability, robustness and theoretical characteristics of the MSMEFC have been detailed and completely analyzed. Furthermore, for coupled nonlinear control system, a further resolution strategy of input-output linearization minimum sliding mode error feedback control(I/OMSMEFC) is also developed. The attitude control and satellite formation control are employed to simulate that the new proposed controllers has been signigicant improved in the convergence speed and accuracy over the traditional sliding mode control.In the appendix of this thesis, a new linearized spacecraft formation flying dynamic model is proposed and derived under the influence of J2 and atmospheric drag in a small eccentrincity orbit/circular orbit. The accuracy and precision of the proposed linearized dynamical model has been verified and analyzed, which provides the mathematical model for the numerical simulations in the several chapters.In this thesis, the estimation and control problems of the spacecraft attitude and spacecraft formation flying have been employed for the application objects, respectively. It is shown that the simulation results are consistent with the theoretical analysis of the proposed filters and controllers. By comparison with the traditional methods, it is clear that the proposed theoretical methods have obvious advantages. The investigated achievements in this thesis can be carried out to the industrial production, equipment development(linear and nonlinear systems); thereby having broad prospects for engineering applications.