In this paper,the authors revisit decentralized control of linear quadratic(LQ)systems.Instead of imposing an assumption that the process and observation noises are Gaussian,the authors assume that the controllers are...In this paper,the authors revisit decentralized control of linear quadratic(LQ)systems.Instead of imposing an assumption that the process and observation noises are Gaussian,the authors assume that the controllers are restricted to be linear.The authors show that the multiple decentralized control models,the form of the best linear controllers is identical to the optimal controllers obtained under the Gaussian noise assumption.The main contribution of the paper is the solution technique.Traditionally,optimal controllers for decentralized LQ systems are identified using dynamic programming,maximum principle,or spectral decomposition.The authors present an alternative approach which is based by combining elementary building blocks from linear systems,namely,completion of squares,state splitting,static reduction,orthogonal projection,(conditional)independence of state processes,and decentralized estimation.展开更多
The main results of this paper are as follows: （ⅰ） The important formulas, given by Bautin, of three focal quantities for the specific form of quadratle system （E2） have been generalized to the general form of ...The main results of this paper are as follows: （ⅰ） The important formulas, given by Bautin, of three focal quantities for the specific form of quadratle system （E2） have been generalized to the general form of （E2）. （ⅱ） By using the method in [13], a kind of （E2） possessing at least four limit cycles is given. Theorem 2 herein contains the results in [11--13] on （1,3）-distribution of limit cycles of （E2）.展开更多
In a previous paper, we have proved that a planar quadratic system with invariant parabola r has at most one limit cycle. In this paper, we use geometric characteristics to give necessary and sufficient conditions un&...In a previous paper, we have proved that a planar quadratic system with invariant parabola r has at most one limit cycle. In this paper, we use geometric characteristics to give necessary and sufficient conditions un'der which a PQSp with three non-degenerate singular points can be transformed into twO different definite forms. In this wayl we obtain all the bifurcations of such a system.展开更多
A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed.Five mechanical properties are adopted to determine the coefficients ...A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed.Five mechanical properties are adopted to determine the coefficients of each part of the yield function.For particular cases,the proposed yield function can be simplified to Mises or Hill’s quadratic yield function.The anisotropic mechanical properties are expressed by defining an angle between the current normalized principal stress space and the reference direction with the assumption of orthotropic anisotropy.The accuracy of the proposed yield function in describing the anisotropy under tension and compression is demonstrated.展开更多
The authors investigate a kind of degenerate quadratic Hamiltonian systems with saddle-loop. Under quadratic perturbations, it is proved that the perturbed system has at most two limit cycles in the finite plane. The ...The authors investigate a kind of degenerate quadratic Hamiltonian systems with saddle-loop. Under quadratic perturbations, it is proved that the perturbed system has at most two limit cycles in the finite plane. The proof relies on a careful analysis of a related Abelian integral.展开更多
基金supported in part by the Natural Sciences and Engineering Research Council of Canada(NSERC)Discovery Grant under Grant No.RGPIN-2021-0351.
文摘In this paper,the authors revisit decentralized control of linear quadratic(LQ)systems.Instead of imposing an assumption that the process and observation noises are Gaussian,the authors assume that the controllers are restricted to be linear.The authors show that the multiple decentralized control models,the form of the best linear controllers is identical to the optimal controllers obtained under the Gaussian noise assumption.The main contribution of the paper is the solution technique.Traditionally,optimal controllers for decentralized LQ systems are identified using dynamic programming,maximum principle,or spectral decomposition.The authors present an alternative approach which is based by combining elementary building blocks from linear systems,namely,completion of squares,state splitting,static reduction,orthogonal projection,(conditional)independence of state processes,and decentralized estimation.
文摘The main results of this paper are as follows: （ⅰ） The important formulas, given by Bautin, of three focal quantities for the specific form of quadratle system （E2） have been generalized to the general form of （E2）. （ⅱ） By using the method in [13], a kind of （E2） possessing at least four limit cycles is given. Theorem 2 herein contains the results in [11--13] on （1,3）-distribution of limit cycles of （E2）.
文摘In a previous paper, we have proved that a planar quadratic system with invariant parabola r has at most one limit cycle. In this paper, we use geometric characteristics to give necessary and sufficient conditions un'der which a PQSp with three non-degenerate singular points can be transformed into twO different definite forms. In this wayl we obtain all the bifurcations of such a system.
基金supported by the National Natural Science Foundation of China (Grant Nos.51475003 and 51205004)Beijing Natural Science Foundation (Grant No.3152010)+1 种基金open project of "State Key Laboratory of Solidification Processing" of Northwestern Polytechnical University (No.SKLSP201635)Beijing Education Committee Science and Technology Program (Grant No.KM201510009004)
文摘A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed.Five mechanical properties are adopted to determine the coefficients of each part of the yield function.For particular cases,the proposed yield function can be simplified to Mises or Hill’s quadratic yield function.The anisotropic mechanical properties are expressed by defining an angle between the current normalized principal stress space and the reference direction with the assumption of orthotropic anisotropy.The accuracy of the proposed yield function in describing the anisotropy under tension and compression is demonstrated.
基金the National Natural Science Foundation of China (No.10101031. No. 10071097). Guangdong Natural Science Foundation (No. 001289)
文摘The authors investigate a kind of degenerate quadratic Hamiltonian systems with saddle-loop. Under quadratic perturbations, it is proved that the perturbed system has at most two limit cycles in the finite plane. The proof relies on a careful analysis of a related Abelian integral.
