An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.     

Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

In this paper, we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control problems. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive $L^2$ and $L^\infty$-error estimates for the control variable. Moreover, using a recovery operator, we also derive some superconvergence results for the control variable. Finally, a numerical example is given to demonstrate the theoretical results.     

Controlling spatio-temporal extreme events by decreasing the localized energy

The problem of controlling extreme events in spatially extended dynamical systems is investigated in this Letter. Based on observations of the system state, the control technique we proposed locally decreases the spatial energy of the amplitude in the vicinity of the highest burst, without needs of any knowledge or prediction of the system model. Considering the specific Complex Ginzburg-Landau equation, we provide theoretical analysis for designing the localized state feedback controller. More exactly, a simple control law by varying a damping parameter at control region is chose to achieve the control. Numerical simulations and statistic analysis demonstrate that extreme events can be efficiently suppressed by our strategy. In particular, the cost of the control and the tolerant time delay in applying the control is considered in detail.     

Closed-loop control of epileptiform activities in a neural population model using a proportional-derivative controller

Epilepsy is believed to be caused by a lack of balance between excitation and inhibitation in the brain. A promising strategy for the control of the disease is closed-loop brain stimulation. How to determine the stimulation control parameters for effective and safe treatment protocols remains, however, an unsolved question. To constrain the complex dynamics of the biological brain, we use a neural population model(NPM). We propose that a proportional-derivative(PD) type closed-loop control can successfully suppress epileptiform activities. First, we determine the stability of root loci, which reveals that the dynamical mechanism underlying epilepsy in the NPM is the loss of homeostatic control caused by the lack of balance between excitation and inhibition. Then, we design a PD type closed-loop controller to stabilize the unstable NPM such that the homeostatic equilibriums are maintained; we show that epileptiform activities are successfully suppressed. A graphical approach is employed to determine the stabilizing region of the PD controller in the parameter space, providing a theoretical guideline for the selection of the PD control parameters. Furthermore, we establish the relationship between the control parameters and the model parameters in the form of stabilizing regions to help understand the mechanism of suppressing epileptiform activities in the NPM. Simulations show that the PD-type closed-loop control strategy can effectively suppress epileptiform activities in the NPM.     

简易旋转倒立摆及控制装置的系统设计简

采用ATmega128作为本旋转倒立摆控制装置的主控芯片,通过直流电机对旋转臂进行控制,实现对摆杆的旋转控制。用编码器对摆杆旋转角度进行测量,将旋转位移转换成数字脉冲实现控制。通过对编码器设定零点,运用PID算法实现精确控制摆杆的摆动角度与状态。测试结果表明,该简易旋转倒立摆及控制装置的系统设计方法科学,具有性能稳定、抗干扰能力强、控制精确,可靠性高,节能环保等优点。     

Protecting Quantum State in Time‐Dependent Decoherence‐Free Subspaces Without the Rotating‐Wave Approximation

In this paper, we propose a scheme to protect quantum state by utilizing the time‐dependent decoherence‐free subspaces (TDFSs) theory without the rotating‐wave approximation (RWA). A coherent control is designed to drive the quantum system into the TDFSs, moreover, the singularities of the designed coherent control can be avoided by appropriately choosing the control parameters. From an experimental view point, the influences of variations of the control parameters and the imperfect initial state are discussed in detail. Numerical simulations confirm that the scheme can protect the quantum information from both the environmental decoherence and the control errors. In addition, by comparing with the scheme employing RWA, we show that the weak coherent control field is not suitable to create the TDFS, the counter‐rotating terms in the strong coherent control are helpful to protect the quantum information.     

Suppression of spatiotemporal chaos under a constant electric potential signal

Suppression of spatiotemporal chaos in a one-dimensional nonlinear drift-wave equation driven by a sinusoidal wave is considered. Using a constant electric potential signal we demonstrate numerically that the spatiotemporal chaos can be effectively suppressed if the control parameters are properly chosen. The threshold and the controllable range of the control parameters are given. By establishing the kinetic equation of the system energy we find theoretically that an additional driving term in the energy equation is produced by the control signal and it can lead up to the frequency entrainment. Moreover, when the regular state is reached under the control, the system energy oscillates quasi-periodically, while the additional driving term decays to zero.     

Adiabatic evolution under quantum control

One difficulty with adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation, we design one of the schemes without any explicit knowledge of the instantaneous eigenstates of the final Hamiltonian. Whereas in another scheme, we assume that the ground state of the Hamiltonian is known, and this information can be used to design the control. By these techniques, a linear speed-up proportional to the nonlinearity can be predicted. As an illustration, we study a two-level system driven by a time-dependent magnetic field under the control. The problem of finding an item in an unsorted database by adiabatic evolution is also examined. The physics behind the control scheme is interpreted.     

耦合映象格子中时空混沌的控制

采用相同的相空间压缩方法,有效地控制了均匀及非均匀耦合映象格子中的时空混沌.数值模拟结果表明,在一定的相空间压缩参数区域内,控制时空混沌到均匀稳定状态时,控制结果与控制参数之间存在确定的函数关系.利用这个控制方程,选择不同的相空间压缩参数控制耦合映象格子中的时空混沌,获得了各种所需要的稳定斑图 关键词： 时空混沌 耦合映象格子     

Stabilization strategy of a car-following model with multiple time delays of the drivers

An extended car-following model with multiple delays is constructed to describe driver's driving behavior. Through stability analysis, the stability condition of this uncontrolled model is given. To dampen the negative impact of the driver's multiple delays (i.e., stability condition is not satisfied), a novel control strategy is proposed to assist the driver in adjusting vehicle operation. The control strategy consists of two parts:the design of control term as well as the design of the parameters in the term. Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms. In the course of the design of parameters in the control term, we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation, which can determine the appropriate parameters in the control terms more quickly. Finally, in the case study, we validate the control strategy by utilizing measured data and configuring scenario, which is closer to the actual traffic. The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver's delays.     

Topological transition by dielectric control of exciton wavefunction in thin nanotube structure

Dielectric control of the topology of an exciton wavefunction is proposed and investigated theoretically. As we have shown in a previous paper, we can change the topology of an exciton wavefunction in a nanotube structure by controlling the length and radius of the nanotube. This nature yields a new device which utilizes the topology of an exciton wavefunction, however, its control via the structural parameters does not suit it to device applications. We found that the in-situ control can be achieved by changing the ambient dielectric constants of the nanotube structure and we calculated the transition condition of the topology of an exciton wavefunction.     

Control of chaos in Frenkel–Kontorova model using reinforcement learning

It is shown that we can control spatiotemporal chaos in the Frenkel–Kontorova(FK) model by a model-free control method based on reinforcement learning. The method uses Q-learning to find optimal control strategies based on the reward feedback from the environment that maximizes its performance. The optimal control strategies are recorded in a Q-table and then employed to implement controllers. The advantage of the method is that it does not require an explicit knowledge of the system, target states, and unstable periodic orbits. All that we need is the parameters that we are trying to control and an unknown simulation model that represents the interactive environment. To control the FK model, we employ the perturbation policy on two different kinds of parameters, i.e., the pendulum lengths and the phase angles. We show that both of the two perturbation techniques, i.e., changing the lengths and changing their phase angles, can suppress chaos in the system and make it create the periodic patterns. The form of patterns depends on the initial values of the angular displacements and velocities. In particular, we show that the pinning control strategy, which only changes a small number of lengths or phase angles, can be put into effect.     

Commande floue et thermique du bâtiment. Proposition d'une loi de chauffe adaptée à la régulation des bâtiments de type tertiaire à occupation discontinue

Fuzzy control and thermal properties of buildings: proposition of a heating law fitting the regulation of tertiary buildings with intermittence. In this article, we start with a general presentation of thermal regulation in buildings and of fuzzy logic applied to the control. Then, thanks to the numerical simulation of a building, we show why regulators based on the use of a straight line heating law are not adapted to the practice of intermittence. The command law we propose is based on fuzzy control. It takes into account both the exterior temperature and the thermal state of the building we estimate by means of the same function whatever the building. Simulating the opening of a window, we show that the closing degree of the regulation loop is very weak. The inference system incorporates constraints upon the conclusions which allow to do an off-line learning from the second week (respect of the open-loop) without any risk of obtaining an aberrant power because of a non-learned rule. The regulation we obtain limits considerably the disfunctioning caused by the open-loop control with intermittent regime. We conclude upon the interest of fuzzy control as regards to the temperature regulation of complex dynamic systems.     

Harnessing symmetry to control quantum transport

Controlling transport in quantum systems holds the key to many promising quantum technologies. Here we review the power of symmetry as a resource to manipulate quantum transport and apply these ideas to engineer novel quantum devices. Using tools from open quantum systems and large deviation theory, we show that symmetry-mediated control of transport is enabled by a pair of twin dynamic phase transitions in current statistics, accompanied by a coexistence of different transport channels. By playing with the symmetry decomposition of the initial state, one can modulate the importance of the different transport channels and hence control the flowing current. Motivated by the problem of energy harvesting, we illustrate these ideas in open quantum networks, an analysis that leads to the design of a symmetry-controlled quantum thermal switch. We review an experimental setup recently proposed for symmetry-mediated quantum control in the lab based on a linear array of atom-doped optical cavities, and the possibility of using transport as a probe to uncover hidden symmetries, as recently demonstrated in molecular junctions, is also discussed. Other symmetry-mediated control mechanisms are also described. Overall, these results demonstrate the importance of symmetry not only as an organizing principle in physics but also as a tool to control quantum systems.     

Prediction-based control of chaos

Pyragas proposes a practically useful control method, called delayed feedback control, for control of chaos. Conditions for (local) stabilization by the delayed feedback control, however, are more restricted than those by the OGY method. In order to overcome this problem, we propose a novel control method, called a prediction-based feedback control, for discrete-time chaotic systems. Moreover, we give necessary and sufficient conditions for exponential stabilization of fixed points by the proposed method.     

脉冲激光烧蚀中电声弛豫时间的确定

为了提高脉冲激光制备薄膜的质量,准确掌握电声弛豫时间是关键,它对脉冲激光脉宽和能量密度的选取起着决定性的作用. 文中以铝靶材为例,利用经典的双温方程通过时域有限差分法(FDTD)得到电子、离子亚系统的温度随时间和位置演化的图像,进而得到电声弛豫时间的准确值. 这样便能准确划分热烧蚀和非平衡烧蚀,从而更好地控制激光的烧蚀过程. 同时找出了电声弛豫时间随激光脉宽以及能量密度变化的规律. 关键词： 飞秒激光 电声弛豫时间 双温方程 激光能量密度     

不确定动态混沌系统的最优控制

对于混沌系统的控制问题,考虑到控制系统能量限制的要求,首先确立一个二次目标函数,然后给出了求解最优控制律的一个简单方法,该方法通过求解线性二次最优控制问题,获得了混沌系统的最优控制律,避免了求解非线性Hamilton-Jacobi-Bellman偏微分方程(HJB方程)的困难.利用Lyapunov方法证明了闭环系统的稳定性.对统一混沌系统和Liu混沌系统的仿真结果表明了控制策略的有效性.     

一类新混沌系统的线性状态反馈控制

研究了一类新混沌系统的控制问题.利用Routh-Hurwitz准则对受控系统进行了稳定性分析，结合线性状态反馈方法理论上严格证明了达到控制目标反馈系数的选择原则.数值研究证明了该方法能够有效地控制混沌系统到失稳的平衡点或周期解，同时控制效果在弱噪声干扰下具有很强的鲁棒性. 关键词： 新混沌系统 线性状态反馈控制 Routh-Hurwitz准则 噪声     

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.     

不确定动态混沌系统的最优控制

对于混沌系统的控制问题,考虑到控制系统能量限制的要求,首先确立一个二次目标函数,然后给出了求解最优控制律的一个简单方法,该方法通过求解线性二次最优控制问题,获得了混沌系统的最优控制律,避免了求解非线性Hamilton-Jacobi-Bellman 偏微分方程(HJB方程)的困难.利用Lyapunov方法证明了闭环系统的稳定性.对统一混沌系统和Liu混沌系统的仿真结果表明了控制策略的有效性.