自适应光学系统几种随机并行优化控制算法比较

 直接对系统性能指标进行优化是自适应光学系统中一种重要的波前畸变校正方法,选择合适的随机并行优化控制算法是该技术成功实现的关键。以32单元变形镜为校正器,基于多种随机并行优化算法建立自适应光学系统仿真模型。从算法的收敛速度、校正效果、局部极值3个方面对遗传算法、单向扰动随机并行梯度下降、双向扰动随机并行梯度下降及模拟退火算法进行了比较。仿真结果表明,遗传算法收敛速度太慢,不适用于需要实时控制的自适应光学系统;双向扰动随机并行梯度下降算法收敛速度、校正效果要优于单向扰动随机并行梯度下降,且能够适应各种情况下的扰动电压;模拟退火几乎以概率1收敛到全局极值附近,且收敛速度是上述算法中最快的。     

Phase retrieval using the transport of intensity equation solved by the FMG–CG method

The relationship between the object-plane phase and the intensity distribution in the Fresnel region can be described by the transport of intensity equation (TIE). The phase distribution can thus be uniquely determined by solving TIE. In this study, a full multigrid preconditioned conjugate gradient (FMG–CG) method is proposed to numerically solve the TIE for phase retrieval. The full multigrid method is a scalable algorithm, and can be parallelized readily and efficiently. By using this method as a preconditioner of the preconditioned conjugate gradient (PCG) method, fast convergence is obtained. The simulation experiments show that complicated phase distributions with fast convergence speed can be retrieved by this composite method.     

Dynamics of Coordinate Ascent Variational Inference: A Case Study in 2D Ising Models

Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study the convergence of coordinate ascent algorithms for mean field variational inference. Focusing on the Ising model defined on two nodes, we fully characterize the dynamics of the sequential coordinate ascent algorithm and its parallel version. We observe that in the regime where the objective function is convex, both the algorithms are stable and exhibit convergence to the unique fixed point. Our analyses reveal interesting discordances between these two versions of the algorithm in the region when the objective function is non-convex. In fact, the parallel version exhibits a periodic oscillatory behavior which is absent in the sequential version. Drawing intuition from the Markov chain Monte Carlo literature, we empirically show that a parameter expansion of the Ising model, popularly called the Edward–Sokal coupling, leads to an enlargement of the regime of convergence to the global optima.     

An efficient and robust numerical algorithm for estimating parameters in Turing systems

We present a new algorithm for estimating parameters in reaction–diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer–Meinhardt reaction–diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.     

核磁共振中的量子控制

近年来, 随着量子信息科学的发展, 对由量子力学原理描述的微观世界的主动调控已成为重要的前沿研究领域. 为构造实际的量子信息处理器, 一个关键的挑战是: 如何对处于噪声环境下的量子体系实现一系列高精度的任意操作, 以完成目标量子信息处理任务. 为此, 人们将经典系统控制论的思想方法延伸到量子体系的领域, 提出了大量的量子控制方法以及相关的数值技术(如量子优化控制、量子反馈控制等), 并取得了丰富的研究成果. 核磁共振自旋体系具备成熟的系统理论和操控技术, 为量子控制方法的实用性研究提供了优秀的实验测试平台. 因此, 基于核磁共振的量子控制成为量子控制领域的重要方向. 本文简要介绍了量子控制的基本概念和方法; 从系统控制论的角度对核磁共振自旋体系的基本原理和重要控制任务做了阐述; 介绍了近些年来在该领域发展的相关控制方法及其应用; 对基于核磁共振体系的量子控制的进一步的研究做了几点展望.     

Heteronuclear decoupling by optimal tracking

The problem to design efficient heteronuclear decoupling sequences is studied using optimal control methods. A generalized version of the gradient ascent engineering (GRAPE) algorithm is presented that makes it possible to design complex non-periodic decoupling sequences which are characterized by tens of thousands of pulse sequence parameters. In contrast to conventional approaches based on average Hamiltonian theory, the concept of optimal tracking is used: a pulse sequence is designed that steers the evolution of an ensemble of spin systems such that at a series of time points, a specified trajectory of the density operator is tracked as closely as possible. The approach is demonstrated for the case of low-power heteronuclear decoupling in the liquid state for in vivo applications. Compared to conventional sequences, significant gains in decoupling efficiency and robustness with respect to offset and inhomogeneity of the radio-frequency field were found in simulations and experiments.     

Practical pulse engineering: Gradient ascent without matrix exponentiation

Since 2005, there has been a huge growth in the use of engineered control pulses to perform desired quantum operations in systems such as nuclear magnetic resonance quantum information processors. These approaches, which build on the original gradient ascent pulse engineering algorithm, remain computationally intensive because of the need to calculate matrix exponentials for each time step in the control pulse. In this study, we discuss how the propagators for each time step can be approximated using the Trotter–Suzuki formula, and a further speedup achieved by avoiding unnecessary operations. The resulting procedure can provide substantial speed gain with negligible costs in the propagator error, providing a more practical approach to pulse engineering.     

Hybrid approach used for extended image-based wavefront sensor-less adaptive optics

The stochastic parallel gradient descent(SPGD) algorithm is widely used in wavefront sensor-less adaptive optics(WSAO) systems. However, the convergence is relatively slow. Modal-based algorithms usually provide much faster convergence than SPGD; however, the limited actuator stroke of the deformable mirror(DM) often prohibits the sensing of higher-order modes or renders a closed-loop correction inapplicable. Based on a comparative analysis of SPGD and the DM-modal-based algorithm, a hybrid approach involving both algorithms is proposed for extended image-based WSAO, and is demonstrated in this experiment. The hybrid approach can achieve similar correction results to pure SPGD, but with a dramatically decreased iteration number.     

基于Zernike模式的自适应光学系统随机并行梯度下降算法

 控制算法的收敛速度一定程度上限制了无波前探测自适应光学技术在实时波前畸变校正中的应用。从理论分析角度提出将模式法和区域法结合起来以提高算法收敛速度,并以61单元变形镜为校正器,建立基于随机并行梯度下降算法自适应光学系统仿真模型。结果表明：达到同样的校正效果时,采用组合优化的算法收敛速度要明显优于基于区域法的收敛速度,从而验证了理论分析的合理性。     

Preconditioning methods for discontinuous Galerkin solutions of the Navier–Stokes equations

A Newton–Krylov method is developed for the solution of the steady compressible Navier–Stokes equations using a discontinuous Galerkin (DG) discretization on unstructured meshes. Steady-state solutions are obtained using a Newton–Krylov approach where the linear system at each iteration is solved using a restarted GMRES algorithm. Several different preconditioners are examined to achieve fast convergence of the GMRES algorithm. An element Line-Jacobi preconditioner is presented which solves a block-tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(0)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling. This reordering is shown to be superior to standard reordering techniques (Nested Dissection, One-way Dissection, Quotient Minimum Degree, Reverse Cuthill–Mckee) especially for viscous test cases. The Block-ILU(0) factorization is performed in-place and an algorithm is presented for the application of the linearization which reduces both the memory and CPU time over the traditional dual matrix storage format. Additionally, a linear p-multigrid preconditioner is also considered, where Block-Jacobi, Line-Jacobi and Block-ILU(0) are used as smoothers. The linear multigrid preconditioner is shown to significantly improve convergence in term of number of iterations and CPU time compared to a single-level Block-Jacobi or Line-Jacobi preconditioner. Similarly the linear multigrid preconditioner with Block-ILU smoothing is shown to reduce the number of linear iterations to achieve convergence over a single-level Block-ILU(0) preconditioner, though no appreciable improvement in CPU time is shown.     

Improved Particle Swarm Optimization Based on Entropy and Its Application in Implicit Generalized Predictive Control

Setting sights on the problem of input-output constraints in most industrial systems, an implicit generalized predictive control algorithm based on an improved particle swarm optimization algorithm (PSO) is presented in this paper. PSO has the advantages of high precision and fast convergence speed in solving constraint problems. In order to effectively avoid the problems of premature and slow operation in the later stage, combined with the idea of the entropy of system (SR), a new weight attenuation strategy and local jump out optimization strategy are introduced into PSO. The velocity update mechanism is cancelled, and the algorithm is adjusted respectively in the iterative process and after falling into local optimization. The improved PSO is used to optimize the performance index in predictive control. The combination of PSO and gradient optimization for rolling-horizon improves the optimization effect of the algorithm. The simulation results show that the system overshoot is reduced by about 7.5% and the settling time is reduced by about 6% compared with the implicit generalized predictive control algorithm based on particle swarm optimization algorithm (PSO-IGPC).     

一类离散时间广义系统的迭代学习控制

针对一类离散时间广义系统,提出了一种离散迭代学习控制算法.首先,通过非奇异变换将离散时间广义系统分解为正常离散状态方程和代数方程的形式.然后,利用上一次迭代学习获得的前一时刻误差和当前时刻误差来修正上一次的控制量,从而获得下一次迭代学习的新控制量,并对算法的收敛性进行了理论证明,给出了算法收敛的充分条件.研究结果表明,所提算法能够在有限时间区间内实现系统状态对期望状态的完全跟踪.最后,通过仿真算例进一步验证了所提算法的有效性.     

混沌系统控制与同步的细菌觅食和差分进化混合算法

将混沌系统的控制与同步问题转化为函数优化问题,提出CDEM算法.把差分进化算法与细菌觅食算法相融合,提高DE算法的收敛性,并利用遗传变异算子保持种群多样性;利用CDEM算法求解混沌系统的控制与同步问题.以典型的离散混沌系统Hénon Map为例进行数值试验,结果表明算法有效、稳定,并分析各个参数对该算法的影响.     

Design and application of robust rf pulses for toroid cavity NMR spectroscopy

We present robust radio frequency (rf) pulses that tolerate a factor of six inhomogeneity in the B? field, significantly enhancing the potential of toroid cavity resonators for NMR spectroscopic applications. Both point-to-point (PP) and unitary rotation (UR) pulses were optimized for excitation, inversion, and refocusing using the gradient ascent pulse engineering (GRAPE) algorithm based on optimal control theory. In addition, the optimized parameterization (OP) algorithm applied to the adiabatic BIR-4 UR pulse scheme enabled ultra-short (50 μs) pulses with acceptable performance compared to standard implementations. OP also discovered a new class of non-adiabatic pulse shapes with improved performance within the BIR-4 framework. However, none of the OP-BIR4 pulses are competitive with the more generally optimized UR pulses. The advantages of the new pulses are demonstrated in simulations and experiments. In particular, the DQF COSY result presented here represents the first implementation of 2D NMR spectroscopy using a toroid probe.     

An evaluation of the FCT method for high-speed flows on structured overlapping grids

This study considers the development and assessment of a flux-corrected transport (FCT) algorithm for simulating high-speed flows on structured overlapping grids. This class of algorithm shows promise for solving some difficult highly-nonlinear problems where robustness and control of certain features, such as maintaining positive densities, is important. Complex, possibly moving, geometry is treated through the use of structured overlapping grids. Adaptive mesh refinement (AMR) is employed to ensure sharp resolution of discontinuities in an efficient manner. Improvements to the FCT algorithm are proposed for the treatment of strong rarefaction waves as well as rarefaction waves containing a sonic point. Simulation results are obtained for a set of test problems and the convergence characteristics are demonstrated and compared to a high-resolution Godunov method. The problems considered are an isolated shock, an isolated contact, a modified Sod shock tube problem, a two-shock Riemann problem, the Shu–Osher test problem, shock impingement on single cylinder, and irregular Mach reflection of a strong shock striking an inclined plane.     

A spectral FC solver for the compressible Navier–Stokes equations in general domains I: Explicit time-stepping

We present a Fourier continuation (FC) algorithm for the solution of the fully nonlinear compressible Navier–Stokes equations in general spatial domains. The new scheme is based on the recently introduced accelerated FC method, which enables use of highly accurate Fourier expansions as the main building block of general-domain PDE solvers. Previous FC-based PDE solvers are restricted to linear scalar equations with constant coefficients. The FC methodology presented in this text thus constitutes a significant generalization of the previous FC schemes, as it yields general-domain FC solvers for nonlinear systems of PDEs. While not restricted to periodic boundary conditions and therefore applicable to general boundary value problems on arbitrary domains, the proposed algorithm inherits many of the highly desirable properties arising from rapidly convergent Fourier expansions, including high-order convergence, essentially spectrally accurate dispersion relations, and much milder CFL constraints than those imposed by polynomial-based spectral methods—since, for example, the spectral radius of the FC first derivative grows linearly with the number of spatial discretization points. We demonstrate the accuracy and optimal parallel efficiency of the algorithm in a variety of scientific and engineering contexts relevant to fluid-dynamics and nonlinear acoustics.     

自适应光学系统随机并行梯度下降控制算法实验研究

随机并行梯度下降算法是一种极具应用潜力的自适应光学系统控制算法,具有不依赖波前传感器直接对系统性能指标进行优化的特点。基于32单元变形镜、CCD成像器件等建立自适应光学系统随机并行梯度下降控制算法实验平台。考察算法增益系数和扰动幅度对校正效果和收敛速度的影响,验证随机并行梯度下降算法的基本原理。实验结果表明参量选取合适的情况下,随机并行梯度下降控制算法对静态或慢变化的畸变波前具有较好的校正能力。根据实验结果分析了影响随机并行梯度下降算法校正速度的主要因素。     

Computational issues in parameter estimation and feedback control problems for partial differential equation systems

We consider computational aspects of two problems governed by partial differential equations systems: (i) the computation of approximate Riccati feedback gains for LQR control problems,(ii) the estimation of parameters using methods based on approximate gradients computed via a costate algorithm. Sufficient conditions for convergence of algorithms for these problems are discussed; in both cases, some type of adjoint or costate system convergence is required in addition to the expected system convergence. Examples are discussed that illustrate computational difficulties which may arise if only convergence of the approximate system holds (i.e., in the event costate convergence does not hold).     

Improving performance of FxRLS algorithm for active noise control of impulsive noise

Active noise control (ANC) systems employing adaptive filters suffer from stability issues in the presence of impulsive noise. New impulsive noise control algorithms based on filtered-x recursive least square (FxRLS) algorithm are presented. The FxRLS algorithm gives better convergence than the filtered-x least mean square (FxLMS) algorithm and its variants but lacks robustness in the presence of high impulsive noise. In order to improve the robustness of FxRLS algorithm for ANC of impulsive noise, two modifications are suggested. First proposed modification clips the reference and error signals while, the second modification incorporates energy of the error signal in the gain of FxRLS (MGFxRLS) algorithm. The results demonstrate improved stability and robustness of proposed modifications in the FxRLS algorithm. However, another limitation associated with the FxRLS algorithm is its computationally complex nature. In order to reduce the computational load, a hybrid algorithm based on proposed MGFxRLS and normalized step size FxLMS (NSS-FXLMS) is also developed in this paper. The proposed hybrid algorithm combines the stability of NSS-FxLMS algorithm with the fast convergence speed of the proposed MGFxRLS algorithm. The results of the proposed hybrid algorithm prove that its convergence speed is faster than that of NSS-FxLMS algorithm with computational complexity lesser than that of FxRLS algorithm.     

Policy iteration optimal tracking control for chaotic systems by using an adaptive dynamic programming approach

A policy iteration algorithm of adaptive dynamic programming(ADP) is developed to solve the optimal tracking control for a class of discrete-time chaotic systems. By system transformations, the optimal tracking problem is transformed into an optimal regulation one. The policy iteration algorithm for discrete-time chaotic systems is first described. Then,the convergence and admissibility properties of the developed policy iteration algorithm are presented, which show that the transformed chaotic system can be stabilized under an arbitrary iterative control law and the iterative performance index function simultaneously converges to the optimum. By implementing the policy iteration algorithm via neural networks,the developed optimal tracking control scheme for chaotic systems is verified by a simulation.