Nonlinear System Filtering Based On Tensor Product Model Transformation

Nonlinear system filtering has a wide range of applications in the fields of aviation,aerospace,automotive and electronics,etc.,and is one of the important research branches in the systems and control theory.Motivated by the idea of the global linearization,this thesis addresses the nonlinear system filtering problem using the tensor product model transformation?TPMT?and the linear matrix inequality?LMI?theory,with particular attention paid to the TPMT-based polytopic linearization,the conservativeness of the linearization model,the nonlinear system H₂/H_? filtering and the computational complexity of the filter design.Firstly,in order to circumvent the local approximation error and the difficulty of handling nonlinear severity of the local approximation methods,the ploytopic linearization for nonlinear systems is studied.The nonlinear system is converted to quasi linear parameter varying system using the mean value theorem of the vector-valued multivariate functions and the conditions of the polytopic linearization are given.Further,the high-order singular value decomposition-based TPMT is applied to compute the linearization model,which solves the difficulty of the acquisition of the polytopic linearization model.Secondly,the issues concerning the conservativeness of TPMT-based polytopic linearization and the corresponding rectification method are investigated.The methods of describing the conservativeness of the linearization model are proposed using the vertex tensor and the weight matrices in the tensor product model and the conservativeness index is put forward for the first time to quantitatively describing the conservativeness.In order to reduce large conservativeness of the linearization model,the approach to generating candidate rectifications is presented at first and then the conservativeness reduction problem is cast to a combinatorial optimization related to these candidates by using the conservativeness index.Furthermore,considering that the cardinality of the candidates readily explodes combinatorially,an optimized rectification algorithm with heuristic local search and iterative routine is presented to efficiently obtain a rectification result with as less conservativeness as possible.Thirdly,the H₂ and H_? filtering problems for both of the nonlinear continuous-time and discrete-time systems are addressed.In terms of the Gaussian noise and H₂ filtering,a polytopic linearization strategy upon a fixed point is utilized and two types of polytopic filters are considered for the case of stable situation;while for the case of unstable situation,two types of global linearization strategies,i.e.,upon a fixed point and along the estimate curve,are concerned.All of these filtering design methods are available in terms of LMIs.Similarly,in terms of unknown disturbances,both of the stable and unstable circumstances and different polytopic linearization strategies are investigated to design various H_?filters for the nonlinear systems,which avoid solving the partial differential inequalities.Especially,the errors of the TPMT polytopic linearization are brought into consideration,upon which the robust H_? filtering for the nonlinear systems with model uncertainties is presented as well.Finally,the computational complexity problem of the TPMT-based nonlinear system filtering is handled.A pair of new operations of tensor unfolding and folding are defined,upon which a nested TPMT?NTPMT?is further proposed for alleviating the“curse of dimensionality”,which is caused by the fact that the number of vertices acquired by the TPMT is easily increase manyfold with the increase of the dimensionality of the system parameter and the number of the LMIs explodes with the vertex cardinality by at least polynomial degree.The NTPMT performs the tensor unfolding operation and the TPMT repeatedly such that a nested tensor product model is obtained,which reduces the order degree of the vertex tensor as well as the number of the vertices.The NTPMT-based nonlinear H₂/H_? filtering is further discussed and the computational complexity of the filter design is reduced remarkably.