The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if so...The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.展开更多
In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interact...In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost,because both the collective ob ject(such as formation or consensus) and the individual goal of each agent are very important for the overall system.First,we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings.The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation(ARE).It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix.Next,for physically interconnected multi-agent systems,the optimal formation algorithm is presented,and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown.Finally,if the communication topology between agents is fixed,the local feedback gain is obtained from the solution to a quadratic equation with one unknown.The equation is derived from the derivative of the cost function with respect to the local feedback gain.Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.展开更多
In this study,37 derivatives of phorbol esters were synthesized and their anti-HIV-1 activities evaluated,building upon our previous synthesis of 51 phorbol derivatives.12-Para-electron-acceptor-trans-cinnamoyl-13-dec...In this study,37 derivatives of phorbol esters were synthesized and their anti-HIV-1 activities evaluated,building upon our previous synthesis of 51 phorbol derivatives.12-Para-electron-acceptor-trans-cinnamoyl-13-decanoyl phorbol derivatives stood out,demonstrating remarkable anti-HIV-1 activities and inhibitory effects on syncytia formation.These derivatives exhibited a higher safety index compared with the positive control drug.Among them,12-(trans-4-fluorocinnamoyl)-13-decanoyl phorbol,designated as compound 3c,exhibited the most potent anti-HIV-1 activity(EC_(50)2.9 nmol·L^(−1),CC50/EC_(50)11117.24)and significantly inhibited the formation of syncytium(EC_(50)7.0 nmol·L^(−1),CC50/EC_(50)4891.43).Moreover,compound 3c is hypothesized to act both as an HIV-1 entry inhibitor and as an HIV-1 reverse transcriptase inhibitor.Isothermal titration calorimetry and molecular docking studies indicated that compound 3c may also function as a natural activator of protein kinase C(PKC).Therefore,compound 3c emerges as a potential candidate for developing new anti-HIV drugs.展开更多
By Riccati transformation, we establish some oscillation theorems for a class of two-dimensional nonlinear delay differential systems. The results obtained generalize some relatively known results.
The average mass concentration of the aerosols in Beijing during the dust storm in the spring of 2000 was -6000 μg · m-3, -30 times as high as that in the non-dust storm days. The enrichment factors of the pollu...The average mass concentration of the aerosols in Beijing during the dust storm in the spring of 2000 was -6000 μg · m-3, -30 times as high as that in the non-dust storm days. The enrichment factors of the pollution elements As, Sb and Se were higher than those in the non-dust storm days. This indicated that As, Sb and Se resulted from the pollution sources of those areas, through which the dust storm passed during their long-range transport, in addition to the local pollution sources in Beijing. The enrichment factors of the Pb, Zn, Cd and Cu were much less than those in the non-dust storm days, suggesting that the local pollution sources in Beijing area contributed to them mostly. The enrichment factors of elements Al, Fe, Sc, Mn, Na, Ni, Cr, V and Co were close to 1, showing that these elements originated from crust. The concentration of S in the dust storm was -10 μg · m-3,4 times as high as that in non-dust storm. S in the aerosols resulted from the adsorption of gaseous SO2 and the consequent展开更多
文摘The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.
基金supported by the National Natural Science Foundation of China(No.61375072)(50%)the Natural Science Foundation of Zhejiang Province,China(No.LQ16F030005)(50%)
文摘In this paper,three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator(LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost,because both the collective ob ject(such as formation or consensus) and the individual goal of each agent are very important for the overall system.First,we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings.The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation(ARE).It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix.Next,for physically interconnected multi-agent systems,the optimal formation algorithm is presented,and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown.Finally,if the communication topology between agents is fixed,the local feedback gain is obtained from the solution to a quadratic equation with one unknown.The equation is derived from the derivative of the cost function with respect to the local feedback gain.Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.
基金supported by the National Natural Science Foundation of China(Nos.81202882,82060670)Suzhou Science and Technology Planning Project in Jiangsu Province of China(No.SNG2021022)+1 种基金the Priority Academic Program Development of the Jiangsu Higher Education Institutes,China(PAPD)and the Project of Innovative Research Team of Yunnan Province(No.202005AE160005).
文摘In this study,37 derivatives of phorbol esters were synthesized and their anti-HIV-1 activities evaluated,building upon our previous synthesis of 51 phorbol derivatives.12-Para-electron-acceptor-trans-cinnamoyl-13-decanoyl phorbol derivatives stood out,demonstrating remarkable anti-HIV-1 activities and inhibitory effects on syncytia formation.These derivatives exhibited a higher safety index compared with the positive control drug.Among them,12-(trans-4-fluorocinnamoyl)-13-decanoyl phorbol,designated as compound 3c,exhibited the most potent anti-HIV-1 activity(EC_(50)2.9 nmol·L^(−1),CC50/EC_(50)11117.24)and significantly inhibited the formation of syncytium(EC_(50)7.0 nmol·L^(−1),CC50/EC_(50)4891.43).Moreover,compound 3c is hypothesized to act both as an HIV-1 entry inhibitor and as an HIV-1 reverse transcriptase inhibitor.Isothermal titration calorimetry and molecular docking studies indicated that compound 3c may also function as a natural activator of protein kinase C(PKC).Therefore,compound 3c emerges as a potential candidate for developing new anti-HIV drugs.
文摘By Riccati transformation, we establish some oscillation theorems for a class of two-dimensional nonlinear delay differential systems. The results obtained generalize some relatively known results.
文摘The average mass concentration of the aerosols in Beijing during the dust storm in the spring of 2000 was -6000 μg · m-3, -30 times as high as that in the non-dust storm days. The enrichment factors of the pollution elements As, Sb and Se were higher than those in the non-dust storm days. This indicated that As, Sb and Se resulted from the pollution sources of those areas, through which the dust storm passed during their long-range transport, in addition to the local pollution sources in Beijing. The enrichment factors of the Pb, Zn, Cd and Cu were much less than those in the non-dust storm days, suggesting that the local pollution sources in Beijing area contributed to them mostly. The enrichment factors of elements Al, Fe, Sc, Mn, Na, Ni, Cr, V and Co were close to 1, showing that these elements originated from crust. The concentration of S in the dust storm was -10 μg · m-3,4 times as high as that in non-dust storm. S in the aerosols resulted from the adsorption of gaseous SO2 and the consequent
