This paper studies the optimization problem of heterogeneous networks under a timevarying topology.Each agent only accesses to one local objective function,which is nonsmooth.An improved algorithm with noisy measureme...This paper studies the optimization problem of heterogeneous networks under a timevarying topology.Each agent only accesses to one local objective function,which is nonsmooth.An improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all agents.To weaken the effect of these noises,two step sizes are introduced in the control protocol.By graph theory,stochastic analysis and martingale convergence theory,it is proved that if the sub-gradients are uniformly bounded,the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected,then the designed control protocol can force all agents to find the global optimal point almost surely.At last,the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.展开更多
Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epider...Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8＋ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4＋ T-Cells, Dendritic Ceils, CD8＋ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4＋ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality made through Matlab by developing iterative of the drug induced system. Numerical simulations are schemes.展开更多
This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable conve...This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function.First,based on the local information of each agent’s neighborhood,a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed,where these gains only have relations with agents’own states.And then,the original closed-loop system is changed into an equivalent one by taking a coordination transformation.Moreover,it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given.By the theory of Lyapunov stability,it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically.Finally,the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61973329National Key Technology R&D Program of China under Grant No.2021YFD2100605Project of Beijing Municipal University Teacher Team Construction Support Plan under Grant No.BPHR20220104。
文摘This paper studies the optimization problem of heterogeneous networks under a timevarying topology.Each agent only accesses to one local objective function,which is nonsmooth.An improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all agents.To weaken the effect of these noises,two step sizes are introduced in the control protocol.By graph theory,stochastic analysis and martingale convergence theory,it is proved that if the sub-gradients are uniformly bounded,the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected,then the designed control protocol can force all agents to find the global optimal point almost surely.At last,the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.
基金supported by the Council of Scientific and Industrial Research,Government of India under Grant No.38(1320)/12/EMR-II
文摘Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8＋ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4＋ T-Cells, Dendritic Ceils, CD8＋ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4＋ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality made through Matlab by developing iterative of the drug induced system. Numerical simulations are schemes.
基金the National Natural Science Foundation of China under Grant Nos.61973329 and 61772063the Beijing Natural Science Foundation under Grant Nos.Z180005 and 9192008。
文摘This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function.First,based on the local information of each agent’s neighborhood,a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed,where these gains only have relations with agents’own states.And then,the original closed-loop system is changed into an equivalent one by taking a coordination transformation.Moreover,it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given.By the theory of Lyapunov stability,it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically.Finally,the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.
