Bai, Golub and Pan presented a preconditioned Hermitian and skew-Hermitian splitting(PHSS) method [Numerische Mathematik, 2004, 32: 1-32] for non-Hermitian positive semidefinite linear systems. We improve the method t...Bai, Golub and Pan presented a preconditioned Hermitian and skew-Hermitian splitting(PHSS) method [Numerische Mathematik, 2004, 32: 1-32] for non-Hermitian positive semidefinite linear systems. We improve the method to solve saddle point systems whose(1,1) block is a symmetric positive definite M-matrix with a new choice of the preconditioner and compare it with other preconditioners. The results show that the new preconditioner outperforms the previous ones.展开更多
This paper deals with controller parameterisation method of adaptive H∞control for polynomial Hamiltonian systems(PHSs)with disturbances and unknown parameters.We design a simplified controller with a set of tuning p...This paper deals with controller parameterisation method of adaptive H∞control for polynomial Hamiltonian systems(PHSs)with disturbances and unknown parameters.We design a simplified controller with a set of tuning parameters which can guarantee that the systems are adaptive H∞stable by using Hamiltonian function method.Then,a method for solving the set of tuning parameters of the controller with symbolic computation is presented.The proposed parameterisation method avoids solving Hamilton–Jacobi–Issacs(HJI)equations and the obtained controller is easier as compared to some existing ones.Simulation example shows that the controller is effective as it can optimise adaptive H∞control by adjusting tuning parameters.All these results are expected to be of use in the study of adaptive H∞control for nonlinear systems with disturbances and unknown parameters.展开更多
基金Supported by the National Natural Science Foundation of China(11301330)Supported by the Shanghai College Teachers Visiting Abroad for Advanced Study Program(B.60-A101-12-010)Supported by the First-class Discipline of Universities in Shanghai
文摘Bai, Golub and Pan presented a preconditioned Hermitian and skew-Hermitian splitting(PHSS) method [Numerische Mathematik, 2004, 32: 1-32] for non-Hermitian positive semidefinite linear systems. We improve the method to solve saddle point systems whose(1,1) block is a symmetric positive definite M-matrix with a new choice of the preconditioner and compare it with other preconditioners. The results show that the new preconditioner outperforms the previous ones.
基金This work was supported by National Natural Science Foundation of China[61374001]NSFCGD project[U1201252]+1 种基金National High-tech R&D Program(863 Program)[2015AA015408]Guangzhou Education Scientific Research Project[1201534690]。
文摘This paper deals with controller parameterisation method of adaptive H∞control for polynomial Hamiltonian systems(PHSs)with disturbances and unknown parameters.We design a simplified controller with a set of tuning parameters which can guarantee that the systems are adaptive H∞stable by using Hamiltonian function method.Then,a method for solving the set of tuning parameters of the controller with symbolic computation is presented.The proposed parameterisation method avoids solving Hamilton–Jacobi–Issacs(HJI)equations and the obtained controller is easier as compared to some existing ones.Simulation example shows that the controller is effective as it can optimise adaptive H∞control by adjusting tuning parameters.All these results are expected to be of use in the study of adaptive H∞control for nonlinear systems with disturbances and unknown parameters.
