This paper addresses distributed computation Sylvester equations of the form AX+XB=C with fractional order dynamics.By partitioning parameter matrices A,B and C,we transfer the problem of distributed solving Sylvester...This paper addresses distributed computation Sylvester equations of the form AX+XB=C with fractional order dynamics.By partitioning parameter matrices A,B and C,we transfer the problem of distributed solving Sylvester equations as two distributed optimization models and design two fractional order continuous-time algorithms,which have more design freedom and have potential to obtain better convergence performance than that of existing first order algorithms.Then,rewriting distributed algorithms as corresponding frequency distributed models,we design Lyapunov functions and prove that proposed algorithms asymptotically converge to an exact or least squares solution.Finally,we validate the effectiveness of proposed algorithms by providing a numerical example.展开更多
This article investigates the problem of on line parameter estimation for fractionalorder linear systems.Based on the theory of fractional-order calculus,the conventional gradient estimator is extended to the fraction...This article investigates the problem of on line parameter estimation for fractionalorder linear systems.Based on the theory of fractional-order calculus,the conventional gradient estimator is extended to the fractional-order areas.The stability of the estimator and the convergence are analysed using the continuous frequency distributed model and indirect Lyapunov method.Finally,numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.展开更多
基金supported in part by the National Natural Science Foundation of China(Nos.61903027,61973002)in part by the National Postdoctoral Program for Innovative Talents(BX20180346)+1 种基金in part by the General Financial Grant from the China Postdoctoral Science Foundation(2019M660834)in part by the Anhui Provincial Natural Science Foundation(No.2008085J32).
文摘This paper addresses distributed computation Sylvester equations of the form AX+XB=C with fractional order dynamics.By partitioning parameter matrices A,B and C,we transfer the problem of distributed solving Sylvester equations as two distributed optimization models and design two fractional order continuous-time algorithms,which have more design freedom and have potential to obtain better convergence performance than that of existing first order algorithms.Then,rewriting distributed algorithms as corresponding frequency distributed models,we design Lyapunov functions and prove that proposed algorithms asymptotically converge to an exact or least squares solution.Finally,we validate the effectiveness of proposed algorithms by providing a numerical example.
文摘This article investigates the problem of on line parameter estimation for fractionalorder linear systems.Based on the theory of fractional-order calculus,the conventional gradient estimator is extended to the fractional-order areas.The stability of the estimator and the convergence are analysed using the continuous frequency distributed model and indirect Lyapunov method.Finally,numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.
