This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables...This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.展开更多
The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux prof...The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.展开更多
An agile missile with tail fins and pulse thrusters has continuous and discontinuous control inputs.This brings certain difficulty to the autopilot design and stability analysis.Indirect robust control via Theta-D tec...An agile missile with tail fins and pulse thrusters has continuous and discontinuous control inputs.This brings certain difficulty to the autopilot design and stability analysis.Indirect robust control via Theta-D technique is employed to handle this problem.An acceleration tracking system is formulated based on the nonlinear dynamics of agile missile.Considering the dynamics of actuators,there is an error between actual input and computed input.A robust control problem is formed by treating the error as input uncertainty.The robust control is equivalent to a nonlinear quadratic optimal control of the nominal system with a modified performance index including uncertainty bound.Theta-D technique is applied to solve the nonlinear optimal control problem to obtain the final control law.Numerical results show the effectiveness and robustness of the proposed strategy.展开更多
为了弥补汽车被动悬架没有主动控制力的缺陷,设计了一种基于传统被动悬架结构的直线电机式主动悬架。在被动悬架中加入直线电机,可以增加主动悬架的阻尼力,降低汽车的振动。首先,对直线电机的结构进行设计;其次,运用ANSYS/Maxwell磁场...为了弥补汽车被动悬架没有主动控制力的缺陷,设计了一种基于传统被动悬架结构的直线电机式主动悬架。在被动悬架中加入直线电机,可以增加主动悬架的阻尼力,降低汽车的振动。首先,对直线电机的结构进行设计;其次,运用ANSYS/Maxwell磁场分析软件和控制变量法,优化直线电机各部分结构尺寸参数,结果表明,直线电机电磁推力的波动降低了83%,同时稳态推力提升了10%;最后,在MATLAB/Simulink软件中搭建直线电机式主动悬架的仿真模型,使用模糊比例-积分-微分(proportion integral differential,PID)对直线电机式主动悬架系统进行控制,分别在时域和频域进行分析,结果表明,相较于被动悬架,直线电机式主动悬架的车身加速度、悬架动挠度、轮胎动荷载都得到了有效抑制,车身加速度功率谱密度也有了大幅度的降低,有效地提高了车辆平顺性和操纵稳定性。展开更多
基金supported by the National Natural Science Foundation of China(11701214)Shandong Provincial Natural Science Foundation,China(ZR2019MA045).
文摘This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.
基金supported partially by the US NSF CAREER award program (ECCS-0645086)National Natural Science Foundation of China (No.F030119)+2 种基金Zhejiang Provincial Natural Science Foundation of China (Nos.Y1110354, Y6110751)the Fundamental Research Funds for the Central Universities of China (No.1A5000-172210101)the Natural Science Foundation of Ningbo (No.2010A610096)
文摘The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.
基金supported by the National Natural Science Foundation of China(61174203)Aeronautical Science Foundation of China(20110177002)
文摘An agile missile with tail fins and pulse thrusters has continuous and discontinuous control inputs.This brings certain difficulty to the autopilot design and stability analysis.Indirect robust control via Theta-D technique is employed to handle this problem.An acceleration tracking system is formulated based on the nonlinear dynamics of agile missile.Considering the dynamics of actuators,there is an error between actual input and computed input.A robust control problem is formed by treating the error as input uncertainty.The robust control is equivalent to a nonlinear quadratic optimal control of the nominal system with a modified performance index including uncertainty bound.Theta-D technique is applied to solve the nonlinear optimal control problem to obtain the final control law.Numerical results show the effectiveness and robustness of the proposed strategy.
文摘为了弥补汽车被动悬架没有主动控制力的缺陷,设计了一种基于传统被动悬架结构的直线电机式主动悬架。在被动悬架中加入直线电机,可以增加主动悬架的阻尼力,降低汽车的振动。首先,对直线电机的结构进行设计;其次,运用ANSYS/Maxwell磁场分析软件和控制变量法,优化直线电机各部分结构尺寸参数,结果表明,直线电机电磁推力的波动降低了83%,同时稳态推力提升了10%;最后,在MATLAB/Simulink软件中搭建直线电机式主动悬架的仿真模型,使用模糊比例-积分-微分(proportion integral differential,PID)对直线电机式主动悬架系统进行控制,分别在时域和频域进行分析,结果表明,相较于被动悬架,直线电机式主动悬架的车身加速度、悬架动挠度、轮胎动荷载都得到了有效抑制,车身加速度功率谱密度也有了大幅度的降低,有效地提高了车辆平顺性和操纵稳定性。
