不确定Euler–Lagrange多智能体系统经验回放自适应蜂拥控制

针对具有可参数化线性回归的不确定项的Euler–Lagrange多智能体系统, 提出了一种基于经验回放的自适应蜂拥控制算法. 在系统模型中的不确定项可以被分解为已知的回归矩阵和未知的回归参数的情况下, 该算法通过在线辨识未知参数, 降低了传统自适应蜂拥控制算法中估计参数收敛对持续激励条件的要求, 可以有效地提高蜂拥系统的性能. 利用设计的滤波器, 在获得估计参数量与实际参数的误差信息的同时, 可以避免使用系统状态的导数信息. 本文设计的自适应律不仅保证系统达成蜂拥控制的目标, 还通过记录不同时刻的误差信息, 使得系统在满足间断激励的情况下, 保证估计参数收敛于实际值. 通过LaSalle不变集理论对算法进行了分析, 给出了理论证明. 仿真验证了该算法的有效性.     

基于参数估计误差的鲁棒自适应律设计及验证

针对传统自适应控制系统设计的自适应律参数收敛慢进而影响控制系统瞬态性能的问题,研究一类新的基于参数估计误差修正的鲁棒自适应律设计.首先引入滤波操作给出参数估计误差的提取方法,构建出含参数估计误差修正项的自适应律,进而将该自适应律用于控制器设计和分析中,可同时实现控制误差和参数估计误差指数收敛.对比分析了几类传统自适应律和所提出自适应律的收敛性和鲁棒性,并给出了保证参数收敛所需持续激励条件的一种直观、简便的在线判别方法.数值仿真及基于自制三自由度直升机系统俯仰轴实验结果表明,基于参数误差修正的自适应律及控制器可得到优于传统自适应方法的跟踪控制和参数估计性能.     

轮式移动机器人滑移量重建与滑移补偿控制

为解决轮式移动机器人的滑移补偿控制问题,首先推导出车体侧滑角的表达式,然后将时变侧滑角的重建问题转化为对地面特性参数的辨识问题.利用Luenberger观测器设计出自适应辨识律,并证明了当控制输入满足持续激励条件时,可以准确辨识出地面特性参数.基于链式系统模型设计出滑移补偿控制器,在滑移角精确已知的条件下,可以保证位置误差收敛,姿态误差有界.仿真结果表明,基于所设计的自适应辨识律,可以准确地重建出滑移角,提高滑移控制精度.     

一类有色噪声干扰下的随机时变系统学习辨识

讨论由一类时变ARMAX模型描述的动态系统学习辨识问题,提出用于估计有限区间上重复运行时变系统时变参数的学习算法.文中给出最小二乘学习算法的具体形式及实现步骤,并分析所提出学习算法的收敛性.分析结果表明,当重复持续激励条件成立且满足严格正实条件时,提出的学习算法具有重复一致性,即参数估值完全收敛于真值.文中还将结果推广到一类周期时变系统.通过数值仿真,进一步对所提学习算法的有效性进行了验证.     

二值量测误差FIR系统参数迭代辨识

本文考虑了量测数据为二值输出且含量测误差的一类有限脉冲响应(FIR)系统的参数辨识问题, 其中, 量测误差使得二值型量测值有一定概率得到相反的取值. 首先, 对所考虑的 FIR 系统, 给出了参数的极大似然估计(MLE), 证明了在噪声满足一定正则条件下MLE的强收敛性和渐近正态性. 此外, 通过分析似然函数的性质, 给出了一种基于期望最大化(EM)方法的MLE迭代求解算法. 为适应更一般的量测误差情形, 给出了带投影的迭代求解算法, 并从理论上证明了迭代估计序列的有界性. 进一步, 在给定数量的观测下, 得到了似然函数具有唯一最大值点的必要和充分条件, 并在持续激励输入条件下, 证明了迭代估计误差以指数速度收敛到零. 最后, 利用数值模拟结果验证了所提出算法的有效性.     

非零和微分博弈系统的事件触发最优跟踪控制（英文）

近年来,对于具有未知动态的非零和微分博弈系统的跟踪问题,已经得到了讨论,然而这些方法是时间触发的,在传输带宽和计算资源有限的环境下并不适用.针对具有未知动态的连续时间非线性非零和微分博弈系统,本文提出了一种基于积分强化学习的事件触发自适应动态规划方法.该策略受梯度下降法和经验重放技术的启发,利用历史和当前数据更新神经网络权值.该方法提高了神经网络权值的收敛速度,消除了一般文献设计中常用的初始容许控制假设.同时,该算法提出了一种易于在线检查的持续激励条件(通常称为PE),避免了传统的不容易检查的持续激励条件.基于李亚普诺夫理论,证明了跟踪误差和评价神经网络估计误差的一致最终有界性.最后,通过一个数值仿真实例验证了该方法的可行性.     

基于预设时间收敛的分布式优化算法

考虑一类分布式优化问题,其目标是通过局部信息交互,使得局部成本函数之和构成的全局成本函数最小.针对该类问题,通过引入时基发生器(TBG),提出两种基于预设时间收敛的分布式比例积分(PI)优化算法.与现有的基于有限/固定时间收敛的分布式优化算法相比,所提出算法的收敛时间不依赖于系统的初值和参数,且可以任意预先设计.此外,在全局成本函数关于最优值点有限强凸,局部成本函数为可微的凸函数,且具有局部Lipschitz梯度的条件下,通过Lyapunov理论证明了所提算法都能实现预设时间收敛.最后,通过数值仿真验证了所提出算法的有效性.     

基于模糊模型的非线性离散时间系统辨识:算法与性能分析

讨论使用模糊系统方法辨识非线性离散时间系统时,模糊系统模型的构造、逼近性 质以及模型参数的自适应调整算法.研究了该辨识方案的有关性能,对模糊模型的参数误差 和辨识误差进行了分析,并给出了模糊模型参数的估计值收敛到其真实值所需的持续激励条 件.     

基于数据驱动的非线性网络系统自适应迭代学习控制

针对非线性网络控制系统中测量数据的量化及随机丢包问题,给出一种基于数据驱动的自适应迭代学习控制算法.该算法能够保证系统在数据量化、随机丢包以及不确定迭代学习长度等因素的影响下,经过有限次迭代后输出轨迹跟踪误差收敛到零;借助伪偏导线性化方法,将非线性系统转换为线形时变系统形式;在线性系统框架下利用前一批次的系统输出信息更新自适应学习增益.与传统迭代学习控制算法不同的是,该算法无需预知迭代长度的先验信息和控制系统模型信息.最后通过Matlab仿真实验验证所提出算法的有效性.     

随机ADD算法的不确定网络优化研究

传统的网络优化问题通过对偶梯度下降算法来解决,虽然该算法能够以分布式方式来实现,但其收敛速度较慢.加速对偶下降算法(ADD)通过近似牛顿步长的分布式计算,提高了对偶梯度下降算法的收敛速率.但由于通信网络的不确定性,在约束不确定时,该算法的收敛性难以保证.基于此,提出了一种随机形式的ADD算法来解决该网络优化问题.理论上证明了随机ADD算法当不确定性的均方误差有界时,能以较高概率收敛于最优值的一个误差邻域;当给出更严格的不确定性的约束条件时,算法则可以较高概率收敛于最优值.实验结果表明,随机ADD算法的收敛速率比随机梯度下降算法快两个数量级.     

Robust adaptive finite‐time parameter estimation and control for robotic systems

This paper studies adaptive parameter estimation and control for nonlinear robotic systems based on parameter estimation errors. A framework to obtain an expression of the parameter estimation error is proposed first by introducing a set of auxiliary filtered variables. Then three novel adaptive laws driven by the estimation error are presented, where exponential error convergence is proved under the conventional persistent excitation (PE) condition; the direct measurement of the time derivatives of the system states are avoided. The adaptive laws are modified via a sliding mode technique to achieve finite‐time convergence, and an online verification of the alternative PE condition is introduced. Leakage terms, functions of the estimation error, are incorporated into the adaptation laws to avoid windup of the adaptation algorithms. The adaptive algorithm applied to robotic systems permits that tracking control and exact parameter estimation are achieved simultaneously in finite time using a terminal sliding mode (TSM) control law. In this case, the PE condition can be replaced with a sufficient richness requirement of the command signals and thus is verifiable a priori. The potential singularity problem encountered in TSM controls is remedied by introducing a two‐phase control procedure. The robustness of the proposed methods against disturbances is investigated. Simulations based on the ‘Bristol‐Elumotion‐Robotic‐Torso II’ (BERT II) are provided to validate the efficacy of the introduced methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Performance analysis of multi-innovation stochastic Newton recursive algorithms

The stochastic Newton recursive algorithm is studied for system identification. The main advantage of this algorithm is that it has extensive form and may embrace more performance with flexible parameters. The primary problem is that the sample covariance matrix may be singular with numbers of model parameters and (or) no general input signal; such a situation hinders the identification process. Thus, the main contribution is adopting multi-innovation to correct the parameter estimation. This simple approach has been proven to solve the problem effectively and improve the identification accuracy. Combined with multi-innovation theory, two improved stochastic Newton recursive algorithms are then proposed for time-invariant and time-varying systems. The expressions of the parameter estimation error bounds have been derived via convergence analysis. The consistence and bounded convergence conclusions of the corresponding algorithms are drawn in detail, and the effect from innovation length and forgetting factor on the convergence property has been explained. The final illustrative examples demonstrate the effectiveness and the convergence properties of the recursive algorithms.     

On parameter convergence in least squares identification and adaptive control

Least squares estimation is appealing in performance and robustness improvements of adaptive control. A strict condition termed persistent excitation (PE) needs to be satisfied to achieve parameter convergence in least squares estimation. This paper proposes a least squares identification and adaptive control strategy to achieve parameter convergence without the PE condition. A modified modeling error that utilizes online historical data together with instant data is constructed as additional feedback to update parameter estimates, and an integral transformation is introduced to avoid the time derivation of plant states in the modified modeling error. On the basis of these results, a regressor filtering–free least squares estimation law is proposed to guarantee exponential parameter convergence by an interval excitation condition, which is much weaker than the PE condition. And then, an identification‐based indirect adaptive control law is proposed to establish exponential stability of the closed‐loop system under the interval excitation condition. Illustrative results considering both identification and control problems have verified the effectiveness and superiority of the proposed approach.     

Adaptive parameter identification of linear SISO systems with unknown time-delay

An adaptive online parameter identification is proposed for linear single-input-single-output (SISO) time-delay systems to simultaneously estimate the unknown time-delay and other parameters. After representing the system as a parameterized form, a novel adaptive law is developed, which is driven by appropriate parameter estimation error information. Consequently, the identification error convergence can be proved under the conventional persistent excitation (PE) condition, which can be online tested in this paper. A finite-time (FT) identification scheme is further studied by incorporating the sliding mode scheme into the adaptation to achieve FT error convergence. The previously imposed constraint on the system relative degree is removed and the derivatives of the input and output are not required. Comparative simulation examples are provided to demonstrate the validity and efficacy of the proposed algorithms.     

Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises

The consistency of identification algorithms for systems with colored noises is a main topic in system identification. This paper focuses on the extended stochastic gradient (ESG) identification algorithm for the multivariable linear systems with moving average noises. By integrating the noise regression terms and the noise model parameters into the information matrix and the parameter vector, and based on the gradient search principle, the ESG algorithm is presented. The unknown noise terms in the information matrix are replaced with their estimates. The convergence analysis shows that the parameter estimation error converges to zero under a persistent excitation condition. Two simulation examples are given to illustrate the effectiveness of the algorithm.     

Composite Adaptive Control of Uncertain Euler‐Lagrange Systems with Parameter Convergence without PE Condition

This work proposes a novel composite adaptive controller for uncertain Euler‐Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.     

A result on exponential tracking error convergence and persistentexcitation

Conditions are investigated for exponential convergence of the tracking error in feedforward adaptive systems having insufficient excitation. Particular attention is paid to the adaptive gradient algorithm with periodic excitation in the overparameterized case. A main result is that for a bounded periodic regressor, the tracking error converges exponentially without regard to parameter convergence or to the degree of overparameterization. These results weaken the persistent excitation (PE) conditions and parameter convergence conditions generally considered necessary to ensure exponential tracking convergence in this class of systems     

Improving transient performance of adaptive control via a modified reference model and novel adaptation

This paper presents a new model reference adaptive control (MRAC) framework for a class of nonlinear systems to address the improvement of transient performance. The main idea is to introduce a nonlinear compensator to reshape the closed‐loop system transient, and to suggest a new adaptive law with guaranteed convergence. The compensator captures the unknown system dynamics and modifies the given nominal reference model and the control action. This modified controlled system can approach the response of the ideal reference model. The transient is easily tuned by a new design parameter of this compensator. The nominal adaptive law is augmented by new leakage terms containing the parameter estimation errors. This allows for fast, smooth and exponential convergence of both the tracking error and parameter estimation, which again improves overall reference model following. We also show that the required excitation condition for the estimation convergence is equivalent to the classical persistent excitation (PE) condition. In this respect, this paper provides an intuitive and numerically feasible approach to online validate the PE condition. The salient feature of the suggested methodology is that the rapid suppression of uncertainties in the controlled system can be achieved without using a large, high‐gain induced, learning rate in the adaptive laws. Extensive simulations are given to show the effectiveness and the improved response of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

Unified treatment of internal model principle based adaptive control algorithms

A number of adaptive control algorithms are summarized here for the control of unknown linear discrete time plants with unknown deterministic disturbances. Adaptive implementation of the internal model principle is used for asymptotical cancellation of the deterministic disturbances. The use of the certainty equivalence principle for implementation of these algorithms can be shown to result in a certain type of unmodelled dynamics error for each of these algorithms. A unified analysis of these algorithms is given under a common framework of unmodelled dynamics. With suitable modification of the parameter estimation algorithm, the global convergence and stability of these algorithms are established without the requirement of the persistency of excitation condition. Some simulation results are provided for support of the analysis.