Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is therefore to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.     

数据驱动的可变精度粗糙集噪音阈值获取方法

可变精度粗糙集理论是经典粗糙集理论的一种扩展理论。它通过引入噪音阈值β,增强了对噪音数据的适应性。然而噪音阂值口多是人为设定,这要求有一定先验知识。提出一种方法,完成了数据驱动的噪音阈值β的自主式获取。仿真实验结果表明,按照此方法获取的噪音阂值β能够提高可变精度粗糙集理论获取知识的性能。     

基于奇异谱分析-灰狼优化-支持向量回归混合模型的黑河正义峡月径流预测

水文预报是水资源优化配置的重要前提,而传统预报方法普遍存在预测精度低的问题,为提高水文预报的准确性,提出了一种混合数据驱动模型用于月径流预测,即奇异谱分析-灰狼优化-支持向量回归(SSA-GWO-SVR)模型。该模型通过SSA对径流数据进行去噪处理来提高径流序列的平稳性和可预测性,采用GWO对SVR模型的参数进行联合选优,从而增强模型的泛化能力。通过黑河正义峡的月径流预测进行模型验证,以平均绝对误差(MAE)、均方根误差(RMSE)、相关系数(R)和纳什效率系数(NSEC)为模型评价标准。实验结果表明该模型的预测精度明显高于自回归积分滑动平均模型(ARIMA)、持续性模型(PM)、交叉验证-SVR(CV-SVR)和GWOSVR模型,并且它能很好地预测径流峰值,说明该模型是一种可靠的径流预测模型,能够更深入地捕获水文径流的内在特性,为基于数据驱动模型的水文预报提供了一种新方法。     

基于数据驱动的故障诊断技术研究现状及展望

对基于数据驱动的过程故障诊断方法进行了总结和划分,其中包含多元统计方法、机器学习方法、流形学习方法等。将各类基于数据驱动的故障诊断方法的原理、研究进展及其在工业过程中的应用进行了描述和分析,最后指出这一领域中需要进一步解决的问题以及近期的研究热点。     

Multi-objective optimization of HVAC system with an evolutionary computation algorithm

A data-mining approach for the optimization of a HVAC (heating, ventilation, and air conditioning) system is presented. A predictive model of the HVAC system is derived by data-mining algorithms, using a dataset collected from an experiment conducted at a research facility. To minimize the energy while maintaining the corresponding IAQ (indoor air quality) within a user-defined range, a multi-objective optimization model is developed. The solutions of this model are set points of the control system derived with an evolutionary computation algorithm. The controllable input variables — supply air temperature and supply air duct static pressure set points — are generated to reduce the energy use. The results produced by the evolutionary computation algorithm show that the control strategy saves energy by optimizing operations of an HVAC system.     

基于数据驱动和统计扩散的树冠提取方法

遥感图像在森林管理中有重要的作用,随着数据量的增加和分辨率的提高,从图像中提取树冠参数成为需要和可能。该文根据树冠的特征,使用标记点过程对树冠建模,采用可逆马尔科夫链蒙特卡罗算法(MCMC)配合模拟退火算法提取树冠的参数,提出新数据项以使其更好适应图像;提出数据驱动的生灭核,同时提出使用随机扩散方法代替非跳转转移核加快算法收敛速度并简化了该方法的实现。最后通过对遥感图像的实验验证了该方法的有效性。     

数据驱动下的矿产预测模型构建方法研究

这是一个计算无处不在、软件定义一切、数据驱动发展的新时代。在矿产预测中,相较于以前统计方法,机器学习、深度学习算法的优势在于能更好地表现出矿化点和空间要素之间的非线性的复杂关系。本文将地质、物探、化探、遥感资料融合在一起,用决策树、支持向量机、卷积神经网络三种算法建模,开展综合信息的矿产预测工作。针对甘肃省北山地区的样本数据,发现相对于卷积神经网络的建模方法,决策树和支持向量机的建模方法更为合适。     

Data driven NARMAX modeling for PEMFC air compressor

Air compressor of proton exchange membrane fuel cell (PEMFC) system is usually nonlinear and strong coupled. It is difficult to establish a online optimization oriented model. In order to solve this problem, this paper proposed a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model for air compressor of PEMFC system. The NARMAX model is an equivalent time-varying linear model, and the time-varying parameters are identified by recurrent neural network (RNN). Simulation results show that the proposed method has small fitting error, the error of air flow and pressure ratio approximate zero, while the mean square error (MSE) of air flow and pressure ratio are 1.5171e-07 and 6.3767e-05, respectively. Therefore, the established air compressor model is accurate and effective.     

Multivariate batch to batch optimisation of fermentation processes incorporating validity constraints

This paper presents an innovative optimisation technique, which utilises an adaptive Multiway Partial Least Squares (MPLS) model to track the dynamics of a batch process from one batch to the next. Utilising this model, an optimisation algorithm solves a quadratic cost function that identifies operating conditions for the subsequent batch that should increase yield. Hard constraints are shown to be required when solving the cost function to ensure that batch conditions do not vary too greatly from one batch to the next. Furthermore, validity constraints are imposed to prevent the PLS model from extrapolating significantly when determining new operating conditions. The capabilities of the proposed technique are illustrated through its application to two benchmark fermentation simulations, where its performance is shown to compare favourably with alternative batch-to-batch optimisation techniques.     

Data-driven output-feedback fault-tolerant L2 control of unknown dynamic systems

This paper studies the data-driven output-feedback fault-tolerant L₂-control problem for unknown dynamic systems. In a framework of active fault-tolerant control (FTC), three issues are addressed, including fault detection, controller reconfiguration for optimal guaranteed cost control, and tracking control. According to the data-driven form of observer-based residual generators, the system state is expressed in the form of the measured input–output data. On this basis, a model-free approach to L₂ control of unknown linear time-invariant (LTI) discrete-time plants is given. To achieve tracking control, a design method for a pre-filter is also presented. With the aid of the aforementioned results and the input–output data-based time-varying value function approximation structure, a data-driven FTC scheme ensuring L₂-gain properties is developed. To illustrate the effectiveness of the proposed methodology, two simulation examples are employed.