This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By i...This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.展开更多
This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles(AUVs) in the presence of wave disturbances. An approximate optimal tracking control(AOTC) approach i...This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles(AUVs) in the presence of wave disturbances. An approximate optimal tracking control(AOTC) approach is proposed. Firstly, a six-degrees-of-freedom(six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value(TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit(REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.展开更多
Fully utilizing the flexibility provided by a district heating system(DHS)can promote wind power accommodation for an electric power system(EPS).However,for privacy or communication reasons,existing power and heat dis...Fully utilizing the flexibility provided by a district heating system(DHS)can promote wind power accommodation for an electric power system(EPS).However,for privacy or communication reasons,existing power and heat dispatch methods are not suitable for practical application.In this paper,a general math formulation of the hierarchical dispatch method is proposed to coordinate EPS and DHS operators based on the feasible region of boundary variables(FRBV),and a method based on the simplicial approximation approach is proposed to obtain a conservative FRBV approximation of a DHS.A simulation based on a real 41-node DHS is constructed to determine the factors that may impact the boundaries of the FRBV,and then the performance of the simplicial approximation approach is displayed by visualizing the approximation process for the FRBV,and finally three dispatch methods are compared to show the advantages of the proposed hierarchical dispatch method.展开更多
基金the National Natural Science Foundation of China(62273058,U22A2045)the Key Science and Technology Projects of Jilin Province(20200401075GX)the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province(20230508043RC)。
文摘This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.
基金supported in part by the National Natural Science Foundation of China (41276085)the Natural Science Foundation of Shandong Province (ZR2015FM004)
文摘This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles(AUVs) in the presence of wave disturbances. An approximate optimal tracking control(AOTC) approach is proposed. Firstly, a six-degrees-of-freedom(six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value(TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit(REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.
基金This work was supported by the National Key Research and Development Program of China under Grant 2017YFB0902100 and State Grid Corporation of China.
文摘Fully utilizing the flexibility provided by a district heating system(DHS)can promote wind power accommodation for an electric power system(EPS).However,for privacy or communication reasons,existing power and heat dispatch methods are not suitable for practical application.In this paper,a general math formulation of the hierarchical dispatch method is proposed to coordinate EPS and DHS operators based on the feasible region of boundary variables(FRBV),and a method based on the simplicial approximation approach is proposed to obtain a conservative FRBV approximation of a DHS.A simulation based on a real 41-node DHS is constructed to determine the factors that may impact the boundaries of the FRBV,and then the performance of the simplicial approximation approach is displayed by visualizing the approximation process for the FRBV,and finally three dispatch methods are compared to show the advantages of the proposed hierarchical dispatch method.