初始分离矩阵优化的在线盲源分离算法

针对在线盲源分离算法收敛速度受初始分离矩阵影响的问题,提出一种基于人工蜂群算法(ABC)的初始分离矩阵优化的在线盲源分离算法。该算法利用人工蜂群算法较强的搜索能力,在盲源分离的初始阶段以批处理的方式进行分离矩阵的寻优,使得算法获得较好的初始迭代点,然后采用梯度下降法以在线的方式实现分离,从而提高算法的整体收敛性能。仿真结果证明了所提算法的有效性,并且其适用于混合矩阵时变的情形。     

Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton–Jacobi equations

In this paper we present an online adaptive control algorithm based on policy iteration reinforcement learning techniques to solve the continuous-time (CT) multi player non-zero-sum (NZS) game with infinite horizon for linear and nonlinear systems. NZS games allow for players to have a cooperative team component and an individual selfish component of strategy. The adaptive algorithm learns online the solution of coupled Riccati equations and coupled Hamilton–Jacobi equations for linear and nonlinear systems respectively. This adaptive control method finds in real-time approximations of the optimal value and the NZS Nash-equilibrium, while also guaranteeing closed-loop stability. The optimal-adaptive algorithm is implemented as a separate actor/critic parametric network approximator structure for every player, and involves simultaneous continuous-time adaptation of the actor/critic networks. A persistence of excitation condition is shown to guarantee convergence of every critic to the actual optimal value function for that player. A detailed mathematical analysis is done for 2-player NZS games. Novel tuning algorithms are given for the actor/critic networks. The convergence to the Nash equilibrium is proven and stability of the system is also guaranteed. This provides optimal adaptive control solutions for both non-zero-sum games and their special case, the zero-sum games. Simulation examples show the effectiveness of the new algorithm.     

Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem

In this paper we discuss an online algorithm based on policy iteration for learning the continuous-time (CT) optimal control solution with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real-time the solution to the optimal control design HJ equation. This method finds in real-time suitable approximations of both the optimal cost and the optimal control policy, while also guaranteeing closed-loop stability. We present an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and critic neural networks. We call this ‘synchronous’ policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for both critic and actor networks, with extra nonstandard terms in the actor tuning law being required to guarantee closed-loop dynamical stability. The convergence to the optimal controller is proven, and the stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm.     

A novel optimal tracking control scheme for a class of discrete-time nonlinear systems using generalised policy iteration adaptive dynamic programming algorithm

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm, called generalised policy iteration ADP algorithm, is developed to solve optimal tracking control problems for discrete-time nonlinear systems. The idea is to use two iteration procedures, including an i-iteration and a j-iteration, to obtain the iterative tracking control laws and the iterative value functions. By system transformation, we first convert the optimal tracking control problem into an optimal regulation problem. Then the generalised policy iteration ADP algorithm, which is a general idea of interacting policy and value iteration algorithms, is introduced to deal with the optimal regulation problem. The convergence and optimality properties of the generalised policy iteration algorithm are analysed. Three neural networks are used to implement the developed algorithm. Finally, simulation examples are given to illustrate the performance of the present algorithm.     

Online solution of nonlinear two‐player zero‐sum games using synchronous policy iteration

The two‐player zero‐sum (ZS) game problem provides the solution to the bounded L₂‐gain problem and so is important for robust control. However, its solution depends on solving a design Hamilton–Jacobi–Isaacs (HJI) equation, which is generally intractable for nonlinear systems. In this paper, we present an online adaptive learning algorithm based on policy iteration to solve the continuous‐time two‐player ZS game with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real time an approximate local solution to the game HJI equation. This method finds, in real time, suitable approximations of the optimal value and the saddle point feedback control policy and disturbance policy, while also guaranteeing closed‐loop stability. The adaptive algorithm is implemented as an actor/critic/disturbance structure that involves simultaneous continuous‐time adaptation of critic, actor, and disturbance neural networks. We call this online gaming algorithm ‘synchronous’ ZS game policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for critic, actor, and disturbance networks. The convergence to the optimal saddle point solution is proven, and stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm in solving the HJI equation online for a linear system and a complex nonlinear system. Copyright © 2011 John Wiley & Sons, Ltd.     

基于改进的鲸鱼优化算法在ELD上的应用

针对电力系统经济负荷分配这一典型的非凸、非线性、组合优化问题,提出一种将基于自适应权重更新策略和差分进化的随机变异策略的鲸鱼优化优化算法(ADWOA)相结合。该算法首先在鲸鱼优化算法中引入了自适应权重来提高WOA的搜索能力,使算法能够在早期执行精细的全局搜索,在后期执行精确的局部搜索,加速寻优算法的迭代,同时由于随机变异策略,会再次更新位置。然后从更新的结果中选择最优位置,以加速种群的收敛,并有效防止种群陷入局部最优将适应度较好的个体信息更快地保留用于下一次鲸鱼优化算法的迭代,提高了求最优解的速度和精度。最后,对多个算法在电力系统经济负荷分配问题进行了测试,验证了基于自适应权重的的鲸鱼优化算法可以更合理地配置电力系统的经济负荷,能够有效找到可行解,避免陷入局部最优,能实现经济负荷的合理分配。     

Adaptive improved natural gradient algorithm for blind source separation

We propose an adaptive improved natural gradient algorithm for blind separation of independent sources. First, inspired by the well-known backpropagation algorithm, we incorporate a momentum term into the natural gradient learning process to accelerate the convergence rate and improve the stability. Then an estimation function for the adaptation of the separation model is obtained to adaptively control a step-size parameter and a momentum factor. The proposed natural gradient algorithm with variable step-size parameter and variable momentum factor is therefore particularly well suited to blind source separation in a time-varying environment, such as an abruptly changing mixing matrix or signal power. The expected improvement in the convergence speed, stability, and tracking ability of the proposed algorithm is demonstrated by extensive simulation results in both time-invariant and time-varying environments. The ability of the proposed algorithm to separate extremely weak or badly scaled sources is also verified. In addition, simulation results show that the proposed algorithm is suitable for separating mixtures of many sources (e.g., the number of sources is 10) in the complete case.     

一种基于NPCA的自适应变步长盲源分离算法

收敛速度和稳定误差是在线盲源分离算法的两个重要的性能指标。为了加快算法的收敛速度,提高算法的跟踪性能,提出一种基于NPCA的自适应变步长盲源分离算法。该算法的迭代步长随着输入信号和混合矩阵的变化而变化,因而具有更好的跟踪性能。仿真结果表明,该算法提高了NPCA算法的收敛速度和跟踪性能。     

Fast adaptive algorithms and networks for class-separability features

In this article, we introduce accelerated algorithms for linear discriminant analysis (LDA) and feature extraction from unimodal multiclass Gaussian data. Current adaptive methods based on the gradient descent optimization technique use a fixed or a monotonically decreasing step size in each iteration, which results in a slow convergence rate. Here, we use a variable step size, optimally computed in each iteration using the steepest descent method, in order to accelerate the convergence of the algorithm. Based on the new adaptive algorithm, we present a self-organizing neural network for adaptive computation of the square root of the inverse covariance matrix (Σ^−1/2) and use it (i) in a network for optimal feature extraction from Gaussian data and (ii) in cascaded form with a principal component analysis network for LDA. Experimental results demonstrate fast convergence and high stability of the algorithm and justify its advantages for on-line pattern recognition applications with stationary and non-stationary input data.     

SINGULARITY COMPUTATION FOR ITERATIVE CONTROL OF NONLINEAR AFFINE SYSTEMS

This paper considers a gradient type of iterative algorithm applied to the open loop control for nonlinear affine systems. The convergence of the algorithm relies on the control signal in each iteration be nonsingular. We present an algorithm for computing the singular control for a general class of nonlinear affine systems. Various nonlinear mechanical systems, including nonholonomic systems, are included as examples.     

Natural gradient-based recursive least-squares algorithm for adaptive blind source separation

This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.     

An iterative algorithm for approximate orthogonalisation of symmetric matrices

In a previous article, one of the authors presented an extension of an iterative approximate orthogonalisation algorithm, due to Z. Kovarik, for arbitrary rectangular matrices. In the present article, we propose a modified version of this extension for the class of arbitrary symmetric matrices. For this new algorithm, the computational effort per iteration is much smaller than for the initial one. We prove its convergence and also derive an error reduction factor per iteration. In the second part of the article, we show that we can eliminate the matrix inversion required by the previous algorithm in each iteration, by replacing it with a polynomial matrix expression. Some numerical experiments are also presented for a collocation discretisation of a first kind integral equation.     

A new self-learning optimal control laws for a class of discrete-time nonlinear systems based on ESN architecture

A novel self-learning optimal control method for a class of discrete-time nonlinear systems is proposed based on iteration adaptive dynamic programming(ADP)algorithm.It is proven that the iteration costate functions converge to the optimal one,and a detailed convergence analysis of the iteration ADP algorithm is given.Furthermore,echo state network(ESN)architecture is used as the approximator of the costate function for each iteration.To ensure the reliability of the ESN approximator,the ESN mean square training error is constrained in the satisfactory range.Two simulation examples are given to demonstrate that the proposed control method has a fast response speed due to the special structure and the fast training process.     

基于GaBP算法的快速潮流计算方法

研究在潮流迭代求解过程中雅可比矩阵方程组的迭代求解方法及其收敛性。首先利用PQ分解法进行潮流迭代求解,并针对求解过程中雅可比矩阵对称且对角占优的特性,对雅可比矩阵方程组采用高斯置信传播算法(GaBP)进行求解,再结合Steffensen加速迭代法以提高GaBP算法的收敛性。对IEEE118、IEEE300节点标准系统和两个波兰互联大规模电力系统进行仿真计算后结果表明：随着系统规模的增长,使用Steffensen加速迭代法进行加速的GaBP算法相对于基于不完全LU的预处理广义极小残余方法(GMRES)具有更好的收敛性,为大规模电力系统潮流计算的快速求解提供了一种新思路。     

A neural-network-based iterative GDHP approach for solving a class of nonlinear optimal control problems with control constraints

In this paper, a novel neural-network-based iterative adaptive dynamic programming (ADP) algorithm is proposed. It aims at solving the optimal control problem of a class of nonlinear discrete-time systems with control constraints. By introducing a generalized nonquadratic functional, the iterative ADP algorithm through globalized dual heuristic programming technique is developed to design optimal controller with convergence analysis. Three neural networks are constructed as parametric structures to facilitate the implementation of the iterative algorithm. They are used for approximating at each iteration the cost function, the optimal control law, and the controlled nonlinear discrete-time system, respectively. A simulation example is also provided to verify the effectiveness of the control scheme in solving the constrained optimal control problem.     

面向光伏MPPT控制策略的改进果蝇算法

局部遮光会降低光伏发电系统的效率。在局部遮光条件下,光伏系统的输出功率特性曲线会产生多个峰值,传统的最大功率跟踪方法不具有全局搜索的能力,其在进行多峰值最大功率跟踪时会失效。果蝇算法(Fruit Fly Optimization Algorithm,FOA)具有全局寻优能力,但是在求解过程中存在收敛速度慢、收敛精度低及容易收敛于局部最优值的问题。文中对果蝇算法进行改进,提出结合自适应lévy飞行步长的Lévy-FOA算法,该算法充分利用Lévy飞行不均匀随机游走的特性,引入自适应步长调整因子,改进了原有算法的位置更新方式,提高了算法的收敛速度以及收敛精度,避免了算法陷入局部极值。文中利用3个标准函数对自适应Lévy-FOA算法的收敛性进行分析,并与普通FOA算法、自适应改进学习因子粒子群算法(Adaptive Particle Swarm Optimization,APSO)进行对比。结果表明,与FOA算法和APSO算法相比,自适应Lévy-FOA算法的平均跟踪时间有较大幅度的减少,平均收敛精度提高了4个数量级。最后,将自适应Lévy-FOA算法应用于光伏最大功率跟踪中。仿真结果显示,在不同的光照条件下,自适应Lévy-FOA算法能够经过较少的迭代实现最大功率跟踪,并且在第一次迭代后就能达到最大功率的90%以上,与其他算法的跟踪效果对比,自适应Lévy-FOA算法具有较短的跟踪时间和较高的跟踪精度,实际寻优能力优越,能够提高光伏系统的输出效率。     

Multivariate adaptive control for a class of nonlinear systems

This paper is concerned with multivariable adaptive control for a class of nonlinear stochastic systems with backlash inputs. A simple weighted adaptive control algorithm is presented for the control of such systems whose linear part possesses an arbitrary interactor matrix and is not necessarily minimum phase. The global convergence of the algorithm is established. Simulation results show that the algorithm has good control performances.     

Online adaptive algorithm for optimal control with integral reinforcement learning

In this paper, we introduce an online algorithm that uses integral reinforcement knowledge for learning the continuous‐time optimal control solution for nonlinear systems with infinite horizon costs and partial knowledge of the system dynamics. This algorithm is a data‐based approach to the solution of the Hamilton–Jacobi–Bellman equation, and it does not require explicit knowledge on the system's drift dynamics. A novel adaptive control algorithm is given that is based on policy iteration and implemented using an actor/critic structure having two adaptive approximator structures. Both actor and critic approximation networks are adapted simultaneously. A persistence of excitation condition is required to guarantee convergence of the critic to the actual optimal value function. Novel adaptive control tuning algorithms are given for both critic and actor networks, with extra terms in the actor tuning law being required to guarantee closed loop dynamical stability. The approximate convergence to the optimal controller is proven, and stability of the system is also guaranteed. Simulation examples support the theoretical result. Copyright © 2013 John Wiley & Sons, Ltd.     

迭代步进值自适应调整的果蝇优化算法

针对传统果蝇优化算法（FOA）收敛精度不高和易陷入局部最优的缺点,提出了一种迭代步进值自适应调整的果蝇优化算法（FOAMR）。在该算法中,引入了果蝇群体速度进化因子和聚集度因子,并将迭代步进值表示为以上2个参数的函数同时定义自适应调整因子。在每次迭代时,算法根据当前果蝇群体速度进化因子和聚集度因子动态调整步进值的大小并通过自适应调整因子动态调整搜索距离的大小。对典型函数的测试结果表明,FOAMR比FOA具有更好的全局搜索能力,同时收敛速度、收敛精度明显提高。     

Adaptive joint bandwidth and power allocation in heterogeneous wireless access environment

Joint bandwidth and power allocation for a multi-radio access(MRA)system in a heterogeneous wireless access environment is studied.Since both the number of users being served by the system and the wireless channel state are time-varying,the optimal resource allocation is no longer a static optimum and will change with the varying network state.Moreover,distributed resource allocation algorithms that require iterative updating and signaling interactions cannot converge in negligible time.Thus,it is unrealistic to assume that the active user number and the wireless channel state remain unchanged during the iterations.In this paper,we propose an adaptive joint bandwidth and power allocation algorithm based on a novel iteration stepsize selection method,which can adapt to the varying network state and accelerate the convergence rate.A distributed solution is also designed for the adaptive joint resource allocation implementation.Numerical results show that the proposed algorithm can not only track the varying optimal resource allocation result much more quickly than a traditional algorithm with fixed iteration stepsize,but can also reduce the data transmission time for users and increase the system throughput.