In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
The Rao-Blackwellized Particle Filter （RBPF） is widely used for high dimensional nonlinear sys- tems, often with a linear Gaussian substructure. However, the RBPF is just a specific method in the class of Rao-Blackw...The Rao-Blackwellized Particle Filter （RBPF） is widely used for high dimensional nonlinear sys- tems, often with a linear Gaussian substructure. However, the RBPF is just a specific method in the class of Rao-Blackwellized Filtering （RBF）. This paper analyzes the recursive structure of the RBF from a more gen- eral perspective. The research starts from a general system model and studies the interconnected relation- ships between the two subspaces during the iterations. The results illustrate the working mechanisms of the RBF with an extensible framework for easily building Rao-Blackwellized algorithms with common nonlinear filters. Several examples are given to illustrate how to build new filters using this framework.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
文摘The Rao-Blackwellized Particle Filter （RBPF） is widely used for high dimensional nonlinear sys- tems, often with a linear Gaussian substructure. However, the RBPF is just a specific method in the class of Rao-Blackwellized Filtering （RBF）. This paper analyzes the recursive structure of the RBF from a more gen- eral perspective. The research starts from a general system model and studies the interconnected relation- ships between the two subspaces during the iterations. The results illustrate the working mechanisms of the RBF with an extensible framework for easily building Rao-Blackwellized algorithms with common nonlinear filters. Several examples are given to illustrate how to build new filters using this framework.
