Let Z=（ Zt）t≥0 be a Bessel process of dimension δ（ δ〉0） starting at zero and let K（t） be a differentiable function on [0,∞） with K（t）〉0 （A↓t≥0）. Then we establish the relationship between L^p-norm o...Let Z=（ Zt）t≥0 be a Bessel process of dimension δ（ δ〉0） starting at zero and let K（t） be a differentiable function on [0,∞） with K（t）〉0 （A↓t≥0）. Then we establish the relationship between L^p-norm of log^1/2（1 ＋δJτ） and L^p-norm of sup Zt[t＋k（t）]^-1/2 （0≤t≤τ） for all stopping times τ and all 0〈p〈＋∞.As an interesting example, we show that ｜｜log^1/2（1＋δLm＋1（τ）｜｜p and ｜｜supZtП[1＋Lj（t]^1/2｜｜p （0≤j≤m,j∈Z;0≤t≤τ） are equivalent with 0〈p〈＋∞ for all stopping times rand all integer numbers m, where the function Lm（t） （t≥0） is inductively defined by Lm＋1（t）=log[ 1 ＋Lm（t）] with L0（t）= 1.展开更多
This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant sys...This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.展开更多
The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the on...The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10571025) and the Key Project of Chinese Ministry of Education (No. 106076)
文摘Let Z=（ Zt）t≥0 be a Bessel process of dimension δ（ δ〉0） starting at zero and let K（t） be a differentiable function on [0,∞） with K（t）〉0 （A↓t≥0）. Then we establish the relationship between L^p-norm of log^1/2（1 ＋δJτ） and L^p-norm of sup Zt[t＋k（t）]^-1/2 （0≤t≤τ） for all stopping times τ and all 0〈p〈＋∞.As an interesting example, we show that ｜｜log^1/2（1＋δLm＋1（τ）｜｜p and ｜｜supZtП[1＋Lj（t]^1/2｜｜p （0≤j≤m,j∈Z;0≤t≤τ） are equivalent with 0〈p〈＋∞ for all stopping times rand all integer numbers m, where the function Lm（t） （t≥0） is inductively defined by Lm＋1（t）=log[ 1 ＋Lm（t）] with L0（t）= 1.
基金supported in part by NSF grants #0552758,#0851709, and #0540179.
文摘This paper considers how to use a group of robots to sense and control a diffusion process.The diffusion process is modeled by a partial differential equation (PDE),which is a both spatially and temporally variant system.The robots can serve as mobile sensors,actuators,or both.Centroidal Voronoi Tessellations based coverage control algorithm is proposed for the cooperative sensing task.For the diffusion control problem,this paper considers spraying control via a group of networked mobile robots equipped with chemical neutralizers,known as smart mobile sprayers or actuators,in a domain of interest having static mesh sensor network for concentration sensing.This paper also introduces the information sharing and consensus strategy when using centroidal Voronoi tessellations algorithm to control a diffusion process.The information is shared not only on where to spray but also on how much to spray among the mobile actuators.Benefits from using CVT and information consensus seeking for sensing and control of a diffusion process are demonstrated in simulation results.
文摘The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.
