In this paper,we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional,with two controllers—one can choose only deterministic time functions,called the deterministic contro...In this paper,we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional,with two controllers—one can choose only deterministic time functions,called the deterministic controller,while the other can choose adapted random processes,called the random controller.The optimal control is shown to exist under suitable assumptions.The optimal control is characterized via a system of fully coupled forward-backward stochastic differential equations(FBSDEs)of mean-field type.We solve the FBSDEs via solutions of two(but decoupled)Riccati equations,and give the respective optimal feedback law for both deterministic and random controllers,using solutions of both Riccati equations.The optimal state satisfies a linear stochastic differential equation(SDE)of mean-field type.Both the singular and infinite time-horizonal cases are also addressed.展开更多
为解决网联汽车由于驾驶员误差存在导致的速度轨迹偏移问题,本文提出一种实时的考虑驾驶员误差的网联混合车队生态驾驶策略。首先通过实车试验采集不同驾驶员的驾驶员误差数据,建立基于马尔可夫链的驾驶员误差模型,用于预测未来一段时...为解决网联汽车由于驾驶员误差存在导致的速度轨迹偏移问题,本文提出一种实时的考虑驾驶员误差的网联混合车队生态驾驶策略。首先通过实车试验采集不同驾驶员的驾驶员误差数据,建立基于马尔可夫链的驾驶员误差模型,用于预测未来一段时间的驾驶员误差。然后以最小化整个车队的燃油消耗为优化目标,将车队速度轨迹优化问题描述为一个最优控制问题,采用快速随机模型预测控制(fast stochastic model predictive control,FSMPC)算法求解车队中网联汽车的最优速度轨迹。仿真和智能网联微缩车试验结果表明,相比于传统的基于快速模型预测控制(fast model predictive control,FMPC)的生态驾驶策略,本文所提出的生态驾驶策略能够有效减小车辆的速度轨迹偏移,并降低整个车队的燃油消耗,且满足实时性要求。展开更多
给定计算机网络中的传输控制协议(transmission control protocol,TCP)流量控制算法,如何确定其稳定域,是网络设计中的一个重要问题.由于网络上控制算法受大量随机因素影响,这相当于对一个由随机微分/差分方程描述的控制系统进行稳定性...给定计算机网络中的传输控制协议(transmission control protocol,TCP)流量控制算法,如何确定其稳定域,是网络设计中的一个重要问题.由于网络上控制算法受大量随机因素影响,这相当于对一个由随机微分/差分方程描述的控制系统进行稳定性分析.目前已有研究大多直接对系统方程取期望,转为讨论期望的稳定性,而简单忽略受控TCP流的随机震荡.本文意在指出这种随机震荡给稳定性带来的不可忽视的影响.本文以TCP/RED(含早期随机检测的TCP流)系统为例,首先,从系统的随机微分方程出发,通过在平衡点处线性化,将系统化为含加乘混合噪声的多维线性时不变系统.然后,给出了分别对应时间连续与离散情况的推广的TCP流量控制方程,即含多噪声源的一次时不变随机微分/差分方程组.接着,对此推广形式,推导了其协方差矩阵所满足的矩阵方程,并在此基础上,得到了协方差矩阵极限渐近稳定的充要条件以及此极限的计算公式.在工程设计中,此条件可以作为系统稳定与否的一个替代判据,方差极限公式可用来估计系统的运动范围.最后,将一般公式应用到具体例子上,展示了考虑方差稳定性后系统稳定域的变化.进一步,仿照确定性系统中的处理方法,本文结论还可推广到非线性系统及时变系统.展开更多
针对受两种随机网络攻击影响的网络控制系统(Networked Control Systems,NCS),在分散事件触发机制下,考虑网络时延,通过选取适当的Lyapunov函数,得到了闭环NCS渐进稳定的充分条件,同时使系统具有混合H_(∞)及被动性能。其次,在稳定性判...针对受两种随机网络攻击影响的网络控制系统(Networked Control Systems,NCS),在分散事件触发机制下,考虑网络时延,通过选取适当的Lyapunov函数,得到了闭环NCS渐进稳定的充分条件,同时使系统具有混合H_(∞)及被动性能。其次,在稳定性判据下,给出控制器的设计方法。分散事件触发机制将传感器和事件触发器进行空间分布式设置,缓解了网络拥堵,攻击影响下混合H_(∞)及被动控制器的设计保证网络安全的同时增强了系统的抗干扰能力。最后,通过Matlab进行仿真,验证了所提方法的有效性。展开更多
In this paper, we consider the dividend optimization problem for a financial corporation with transaction costs. Besides the dividend control, the financial corporation takes proportional reinsurance to reduce risk an...In this paper, we consider the dividend optimization problem for a financial corporation with transaction costs. Besides the dividend control, the financial corporation takes proportional reinsurance to reduce risk and the surplus earns interest at the constant force p 〉 0. Because of the presence of fixed transaction costs, the problem becomes a mixed classical-impulse stochastic control problem. We solve this problem explicitly and construct the value function together with the optimal policy展开更多
基金Lebesgue center of mathematics“Investissements d’avenir”program-ANR-11-LABX-0020-01,by CAESARS-ANR-15-CE05-0024MFG-ANR-16-CE40-0015-01.Tang acknowledges research supported by National Science Foundation of China(Grant No.11631004)Science and Technology Commission of Shanghai Municipality(Grant No.14XD1400400).
文摘In this paper,we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional,with two controllers—one can choose only deterministic time functions,called the deterministic controller,while the other can choose adapted random processes,called the random controller.The optimal control is shown to exist under suitable assumptions.The optimal control is characterized via a system of fully coupled forward-backward stochastic differential equations(FBSDEs)of mean-field type.We solve the FBSDEs via solutions of two(but decoupled)Riccati equations,and give the respective optimal feedback law for both deterministic and random controllers,using solutions of both Riccati equations.The optimal state satisfies a linear stochastic differential equation(SDE)of mean-field type.Both the singular and infinite time-horizonal cases are also addressed.
文摘为解决网联汽车由于驾驶员误差存在导致的速度轨迹偏移问题,本文提出一种实时的考虑驾驶员误差的网联混合车队生态驾驶策略。首先通过实车试验采集不同驾驶员的驾驶员误差数据,建立基于马尔可夫链的驾驶员误差模型,用于预测未来一段时间的驾驶员误差。然后以最小化整个车队的燃油消耗为优化目标,将车队速度轨迹优化问题描述为一个最优控制问题,采用快速随机模型预测控制(fast stochastic model predictive control,FSMPC)算法求解车队中网联汽车的最优速度轨迹。仿真和智能网联微缩车试验结果表明,相比于传统的基于快速模型预测控制(fast model predictive control,FMPC)的生态驾驶策略,本文所提出的生态驾驶策略能够有效减小车辆的速度轨迹偏移,并降低整个车队的燃油消耗,且满足实时性要求。
文摘给定计算机网络中的传输控制协议(transmission control protocol,TCP)流量控制算法,如何确定其稳定域,是网络设计中的一个重要问题.由于网络上控制算法受大量随机因素影响,这相当于对一个由随机微分/差分方程描述的控制系统进行稳定性分析.目前已有研究大多直接对系统方程取期望,转为讨论期望的稳定性,而简单忽略受控TCP流的随机震荡.本文意在指出这种随机震荡给稳定性带来的不可忽视的影响.本文以TCP/RED(含早期随机检测的TCP流)系统为例,首先,从系统的随机微分方程出发,通过在平衡点处线性化,将系统化为含加乘混合噪声的多维线性时不变系统.然后,给出了分别对应时间连续与离散情况的推广的TCP流量控制方程,即含多噪声源的一次时不变随机微分/差分方程组.接着,对此推广形式,推导了其协方差矩阵所满足的矩阵方程,并在此基础上,得到了协方差矩阵极限渐近稳定的充要条件以及此极限的计算公式.在工程设计中,此条件可以作为系统稳定与否的一个替代判据,方差极限公式可用来估计系统的运动范围.最后,将一般公式应用到具体例子上,展示了考虑方差稳定性后系统稳定域的变化.进一步,仿照确定性系统中的处理方法,本文结论还可推广到非线性系统及时变系统.
文摘针对受两种随机网络攻击影响的网络控制系统(Networked Control Systems,NCS),在分散事件触发机制下,考虑网络时延,通过选取适当的Lyapunov函数,得到了闭环NCS渐进稳定的充分条件,同时使系统具有混合H_(∞)及被动性能。其次,在稳定性判据下,给出控制器的设计方法。分散事件触发机制将传感器和事件触发器进行空间分布式设置,缓解了网络拥堵,攻击影响下混合H_(∞)及被动控制器的设计保证网络安全的同时增强了系统的抗干扰能力。最后,通过Matlab进行仿真,验证了所提方法的有效性。
基金The first author was supported by the National Natural Science Foundation of China （Grant Nos. 11001139, 11171164） and the Specialized Research Fund for the Doctoral Program of Higher Education （Grant No. 20100031120002）. The second author was supported by the National Natural Science Foundation of China （Grant No. 11101225）.
文摘In this paper, we consider the dividend optimization problem for a financial corporation with transaction costs. Besides the dividend control, the financial corporation takes proportional reinsurance to reduce risk and the surplus earns interest at the constant force p 〉 0. Because of the presence of fixed transaction costs, the problem becomes a mixed classical-impulse stochastic control problem. We solve this problem explicitly and construct the value function together with the optimal policy
