Optimal Control of Uniformly Heated Granular Fluids in Linear Response

We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously—from a mathematical point of view—prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.     

Privacy-Preserving Design of Scalar LQG Control

This paper studies the agent identity privacy problem in the scalar linear quadratic Gaussian (LQG) control system. The agent identity is a binary hypothesis: Agent A or Agent B. An eavesdropper is assumed to make a hypothesis testing the agent identity based on the intercepted environment state sequence. The privacy risk is measured by the Kullback–Leibler divergence between the probability distributions of state sequences under two hypotheses. By taking into account both the accumulative control reward and privacy risk, an optimization problem of the policy of Agent B is formulated. This paper shows that the optimal deterministic privacy-preserving LQG policy of Agent B is a linear mapping. A sufficient condition is given to guarantee that the optimal deterministic privacy-preserving policy is time-invariant in the asymptotic regime. It is also shown that adding an independent Gaussian random process noise to the linear mapping of the optimal deterministic privacy-preserving policy cannot improve the performance of Agent B. The numerical experiments justify the theoretic results and illustrate the reward–privacy trade-off.     

One-Dimensional Transport Code Modeling of the Divertor-Limiter Region in Tokamaks

A model of the divertor-limiter scrapeoff region has been incorporated into the BALDUR one-dimensional tokamak transport code. Simulations of the proposed Toroidal Fusion Test Reactor (TFTR), and Poloidal Divertor (PDX) experiments and existing Alcator-A tokamak experiments have been carried out for ohmic and neutral beam heated cases. In particular, we have studied how the edge conditions and energy-loss mechanisms in PDX depend upon plasma density, and compared our results with analytic estimates. The sensitivity of the results to changes in the transport coefficients and scrapeoff model is discussed with particular reference to the power loading on the TFTR limiter.     

Optimal UAV Formation Tracking Control with Dynamic Leading Velocity and Network-Induced Delays

With the rapid development of UAV technology, the research of optimal UAV formation tracking has been extensively studied. However, the high maneuverability and dynamic network topology of UAVs make formation tracking control much more difficult. In this paper, considering the highly dynamic features of uncertain time-varying leader velocity and network-induced delays, the optimal formation control algorithms for both near-equilibrium and general dynamic control cases are developed. First, the discrete-time error dynamics of UAV leader–follower models are analyzed. Next, a linear quadratic optimization problem is formulated with the objective of minimizing the errors between the desired and actual states consisting of velocity and position information of the follower. The optimal formation tracking problem of near-equilibrium cases is addressed by using a backward recursion method, and then the results are further extended to the general dynamic case where the leader moves at an uncertain time-varying velocity. Additionally, angle deviations are investigated, and it is proved that the similar state dynamics to the general case can be derived and the principle of control strategy design can be maintained. By using actual real-world data, numerical experiments verify the effectiveness of the proposed optimal UAV formation-tracking algorithm in both near-equilibrium and dynamic control cases in the presence of network-induced delays.     

New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect

A feedback control model of lattice hydrodynamic model is proposed by taking the information of the historic optimal velocity into account for the traffic system. The modern control theory is applied for the linear stability condition with feedback control signal. The result shows that the stability of traffic flow is closely related to the information of the historic optimal velocity. Furthermore, numerical simulations conform that the new feedback control did increase the stability of traffic flow efficiently, which is in accord with theoretical analysis.     

A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems

In this work, we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. The algorithm combines a Moreau-Yosida technique for handling state constraints with a semi-smooth Newton method for solving the optimality systems of the regularized sub-problems. The state and adjoint variables are discretized using continuous piecewise linear finite elements while a variational discretization concept is applied for the control. To perform the adaptive mesh refinements cycle we derive local error estimators which extend the goal-oriented error approach to our setting. The performance of the overall adaptive solver is assessed by numerical examples.     

Calibration of the fir polarimeter on TFTR tokamak

The results of the first Faraday rotation measurement on the TFTR tokamak are presented. Data are reported on ohmic-as well as neutral-beam-heated plasmas including solid pellet injections. The procedure and the results of the calibration, are described. The effects of various errors in the measurements as well as the problem of cross coupling laser beams are studied.     

A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems

In this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent order $\mathcal{O}(h^2+k^2)$ is obtained for the numerical solution in a discrete $L^2$-norm. A numerical experiment is presented to test the theoretical result.     

Joint Optimization of Control Strategy and Energy Consumption for Energy Harvesting WSAN

With the rapid development of wireless sensor technology, recent progress in wireless sensor and actuator networks (WSANs) with energy harvesting provide the possibility for various real-time applications. Meanwhile, extensive research activities are carried out in the fields of efficient energy allocation and control strategy design. However, the joint design considering physical plant control, energy harvesting, and consumption is rarely concerned in existing works. In this paper, in order to enhance system control stability and promote quality of service for the WSAN energy efficiency, a novel three-step joint optimization algorithm is proposed through control strategy and energy management analysis. First, the optimal sampling interval can be obtained based on energy harvesting, consumption, and remaining conditions. Then, the control gain for each sampling interval is derived by using a backward iteration. Finally, the optimal control strategy is determined as a linear function of the current plant states and previous control strategies. The application of UAV formation flight system demonstrates that better system performance and control stability can be achieved by the proposed joint optimization design for all poor, sufficient, and general energy harvesting scenarios.     

The Study of Fueling Method and Particle Confinement Improvement

Several high performance tokamak operation regimes have been achieved experimentally in the experiments with the peaked density profiles. The regimes include the improved Ohmic confinement in ASDEX, the pellet enhanced performance mode in Alcator-C, and the super-shot mode in TFTR. In these regimes, peaked core density profiles are always existent, and almost always go with the internal transport barriers, these barriers generally produced by sheared radial electric field. In addition to enhance confinement, the peaked density profile is also needed for the optimized fusion reaction rate and alpha heating power in tokamak plasma, and combined peaked density profile and peaked temperature profile, would make the ignition condition easy obtained. It is desirable to seek and analyze the density profile control schemes that effectively lead to density profile peaking in particle transports experimental investigation.     

A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems

In this paper, we study the mathematical formulation for an optimal control problem governed by a linear parabolic integro-differential equation and present the optimality conditions. We then set up its weak formulation and the finite element approximation scheme. Based on these we derive the a priori error estimates for its finite element approximation both in $H^1$ and $L^2$ norms. Furthermore, some numerical tests are presented to verify the theoretical results.     

基于最小二乘支持向量机建模的混沌系统控制

提出了基于最小二乘支持向量机（LS-SVMs）建模的混沌系统控制方法.与前向神经网络相比，LS-SVMs的优点是其训练过程遵循结构风险最小化原则，不易发生过拟合现象；它通过解一组线性方程组可得到全局惟一的最优解；LS-SVMs的拓扑结构在训练结束时自动获得而不需要预先确定.该方法不需要被控混沌系统的解析模型，且当测量噪声存在情况下控制仍然有效.以一维和二维非线性映射为例进行数值仿真，表明该方法是有效和可行的. 关键词： 混沌控制 支持向量机 建模     

Investigation of the accumulation of deuterium in carbon-deuterium films from the T-10 tokamak

This paper reports the experimental data obtained on the chemical composition of homogeneous carbon films codeposited with deuterium in the T-10 tokamak, the deuterium distribution over the thickness of the films, and the dependence of the ratio between the atomic concentrations of deuterium and carbon (D/C) on the annealing temperature. The experimental data obtained are compared with the results of similar investigations of carbon-hydrogen films formed in the TFTR tokamak.     

Optimal Control for Quantum Driving of Two-Level Systems

In this paper, the optimal quantum control of two-level systems is studied by the decompositions of SU(2). Using the Pontryagin maximum principle, the minimum time of quantum control is analyzed in detail. The solution scheme of the optimal control function is given in the general case. Finally, two specific cases, which can be applied in many quantum systems, are used to illustrate the scheme, while the corresponding optimal control functions are obtained.     

Control and synchronization of second Julia sets

A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper.With this method,the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved.Control and synchronization of generalized Julia sets are also achieved with this optimal control method.The simulations illustrate the efficacy of this method.     

Burgers方程初边值条件的控制

为将优化控制技巧用于复杂的地球物理环流模型及其它领域,以Burgers方程为模型,描述了初边值条件的优化控制.在一般化的意义上,给出了连续问题及其相应的离散形式.引入伴随变量,并由此导出伴随方程.比较初始控制中不同频率误差对优化控制的影响,分析了用有限观测数据作空间插值后的数据、方法的优化控制能力及效果,并进行了数值实验.     

Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances

The problem of optimal tracking control with zero steady-state error for linear time-delay systems with sinusoidal disturbances is considered. Based on the internal model principle, a disturbance compensator is constructed such that the system with external sinusoidal disturbances is transformed into an augmented system without disturbances. By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance. The obtained optimal tracking control law with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. The accurate linear terms can be obtained by solving a Riccati matrix equation and a Sylvester equation, respectively. The compensation term can be approximately obtained through a recursive algorithm. A numerical simulation shows that the algorithm is effective and easily implemented, and the designed tracking controller is robust with respect to the sinusoidal disturbances.     

四频差动激光陀螺最佳工作点实时控制技术

为了降低四频差动激光陀螺（FMDLG）零偏对外界因素影响的敏感性,采用了最佳工作点实时控制技术。该技术使用色散平衡和稳频偏置的方法,对增益区磁场和失谐频率进行小幅度正弦调制,在FMDLG输出零偏中解调出误差信号,经负反馈控制回路使FMDLG在对外界干扰敏感性最小的唯一最佳工作点下工作。与仅使用光强差进行稳频的传统方法相比,最佳工作点控制技术大大降低了FMDLG的磁敏感度和零偏稳定性,证实了FMDLG最佳工作点实时控制技术的有效性;静态、动态测试实验结果证明了该技术的正确性。     

Experimental evaluation of nonlinearities of small-sized insertable gradient coils

A phase imaging technique is proposed to map out and quantify gradient nonlinearities of small-sized insertable gradient coils, assuming the whole-body system gradients are highly linear in the domain of interest. The theory is developed and simple equations are derived to allow quantification. It is applied to a 4-loop 18-cm diameter cylindrical gradient coil of optimal design. Experimental gradient nonlinearity maps are obtained for different fields of view. Gradient non-linearities are quantified locally and in regions of interest, showing close agreement with model data.     

Density waves in a traffic flow model with reaction-time delay

Density waves are investigated analytically and numerically in the optimal velocity model with reaction-time delay of drivers. The stability condition of this model is obtained by using the linear stability theory. The results show that the decrease of reaction-time delay of drivers leads to the stabilization of traffic flow. The Burgers, Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions respectively. The triangular shock waves, soliton waves and kink-antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams. The numerical simulations are given.