主要学术工作总结与主要文献

一、MFAC理论评述及文献[Comments on MFAC with literature]

MFAC理论分间接型MFAC和直接型MFAC。内容包括新概念：伪偏导数、伪梯度、伪Jacobian矩阵、广义Lipschitz条件等；非线性系统动态线性化方法：包括被控系统、理想控制器、重复过程的紧格式/偏格式/全格式动态线性化数据模型；系列被控对象：SISO/MISO/MIMO/复杂连接系统/重复运行系统等；系列控制系统设计方法：包括自适应控制、预测控制、学习控制以及模块化设计方法等；基于压缩映射原理的稳定性分析新方法；新型鲁棒性定义与鲁棒性分析和设计方法等。目前，MFAC理论是一种全新体制下的数据驱动控制理论与方法，具有完整的理论体系。

MFAC理论与方法突破了现代控制理论基于模型的分析与设计框架，避开了控制理论与方法在理论研究与实际应用中的诸多根本性障碍，经典未建模动力学与鲁棒性等概念，在MFAC框架下不存在。 MFAC框架下的被控对象是虚拟的数据模型、假设条件基于数据、稳定性分析基于压缩映射原理、跟踪误差收敛性基于伪梯度的有界性、鲁棒性针对的是数据噪声和不完备性，这些均与基于模型控制理论有本质差别。另外，经典PID控制、线性时不变系统的自适应控制可被证明是MFAC理论的特例。

 

1、原创性[Originality]

  ◆  原创基本概念，针对SISO系统的伪偏导数（Pseudo Partial Derivative, PPD）或伪梯度（Pseudo Gradient, PG），针对MIMO系统的伪Jaccobian矩阵（Pseudo Jaccobian Matrix,PJM）、分块伪Jaccobian矩阵（Partitioned Pseudo Jaccobian Matrix, PPJM）、无模型自适应控制(Model Free Adaptive Control, MFAC);
  ◆  原创基础数学工具：非线性系统的动态线性化数据模型方法，分别包括SISO/MISO/MIMO非线性系统的紧格式动态线性化（Compact Form Dynamic Linearization, CFDL）数据模型，偏格式动态线性化（Partial Form Dynamic Linearization, PFDL）数据模型，全格式动态线性化（Full Form Dynamic Linearization, FFDL）数据模型；
  ◆ 原创稳定性证明的新假设条件：针对SISO/MISO/MIMO非线性系统广义Lipschitz条件（Generalized Lipschitz Condition），以及原创针对SISO/MISO/MIMO非线性系统MFAC系统的基于压缩映射原理的稳定性证明方法；
  ◆ 原创MFAC鲁棒性概念以及基于统计学的分析方法,数据传输丢包、乱码、噪声扰动对控制系统性能的影响

  ◆  Original basic concepts including, Pseudo Partial Derivative (PPD) or Pseudo Gradient (PG) for unknown SISO non-affine nonlinear system; Pseudo Jaccobian Matrix (PJM）or Partitioned Pseudo Jaccobian Matrix (PPJM）for unknown MIMO non-affine nonlinear system, as well as the coined term “Model Free Adaptive Control (MFAC).”
   ◆ Original basic mathematical tool for system and control theory: the equivalent dynamic linearization data modeling method, including the Compact Form Dynamic Linearization (CFDL), the Partial Form Dynamic Linearization (PFDL), and the Full Form Dynamic Linearization (FFDL), data models for SISO/MISO/MIMO non-affine nonlinear systems
   ◆ Original basic assumption for control system stability analysis: the generalized Lipschitz conditions for SISO/MISO/MIMO non-affine nonlinear systems, and the original stability analysis approaches: the contraction mapping principle based stability analysis approaches rather than the overwhelming Lyapunov function methods for SISO/MISO/MIMO non-affine nonlinear systems.
   ◆ Original robustness concept and its analysis tool: the statistics-based influence analysises on the stability and tracking performance under the data-dropout, packet loss/disorder, or data noise, etc. for SISO/MISO/MIMO non-affine nonlinear systems.

2、系统性 [Integrity]

MFAC方法自从1994年首次被提出以来[1]，经过近30余年的持续努力和发展，现已形成了一整套全新体制的控制理论与方法体系。

MFAC理论包括间接型MFAC方法和直接型MFAC方法。间接型、直接型MFAC方法，其内容体系均是具有如下矩阵式框架结构体系：1）不同受控对象，如SISO、MISO、MIMO、复杂连接、重复运行等各种非线性系统；2）不同非线性系统动态线性化数据模型：紧格式动态线性化数据模型、偏格式动态线性化数据模型、全格式动态线性化数据模型；3）系列动态线性化数据模型参数的估计方法：投影算法、最小二乘算法以及其它是变参数估计算法等；4）不同控制器结构设计方法：如最优控制、预测控制、学习控制等等；

间接型MFAC是基于被控对象非线性动力学模型的动态线性化数据建模方法建立的[1-2]，它具有由表1所示的四维架构构成，不同组合方案就构成不同间接型MFAC控制系统。

表表1 间接型MFAC的四维架构体系 [Tab.1 The systematic framework of Indirect MFAC]

直接型MFAC是基于被控对象数学意义下理想控制器的动态线性化数据建模方法建立的[3]，它将控制系统设计问题，转化为控制器参数辨识问题。直接型MFAC的四维架构见表2，不同方案组合就构成不同直接型MFAC控制系统。

 

表2  直接型MFAC的四维架构体系 [Tab. 2 The systematic framework of Direct MFAC]

MFAC is a novel adaptive control method for unknown non-affine discrete-time nonlinear systems, which was initiated in 1994. The main feature of MFAC is that the control system design needs only the I/O data of the controlled process and does not include any information of the mathematical model. After about 30 years, it has been developed a systematic works. MFAC consists of indirect MFAC and direct MFAC, each kind of MFAC has following four dimensional framework, as follows: 1) Different controlled objects, including SISO/MISO/MIMO/complicated connected/ repetitive operation nonlinear systems; 2) Different dynamic linearization data models for a given nonlinear system, including the compact-form dynamic linearization (CFDL), partial-form dynamic linearization (PFDL), and full-form dynamic linearization(FFDL), data models; 3) Different parameter estimation algorithms for the parameters in the data model, including projection-type algorithms, least-square-type algorithms for the time-varying parameters, etc. 4) Different controller structure designing methods, such as optimal control, predictive control, learning control, etc.

Indirect MFAC has following matrix framework [1-2], shown as following Table 1. Different combination consists of different kinds of indirect MFAC schemes.

Direct MFAC, based on the dynamic linearization data model on the ideal controller for a given unknown nonaffine nonlinear system, is a novel MFAC, which transformed the control system designing problem explicitly into the identification issue of the designed linearized controller parameters, and it also has following matrix framework [3], shown as following Table 2. Different combination consists of different kinds of direct MFAC schemes.

 

3、严谨性 [Correctness]

MFAC理论具有严谨的理论基础，其稳定性有严谨的理论保障。

关于SISO非线性系统基于CFDL数据模型的MFAC控制系统设计、稳定性证明见[1,4]。针对SISO系统基于CFDL数据模型和PFDL数据模型的MFAC控制系统设计的稳定性证明见文献[5]。文献[6]则给出了SISO非线性系统基于FFDL数据模型的MFAC控制系统设计稳定性证明。文献[7-8]一起建立了关于MIMO非线性系统MFAC的稳定性理论体系。

SISO非线性系统和MIMO非线性系统的MFAC一起，构成了具有理论严谨性的MFAC控制理论体系。

MFAC系统稳定性证明是基于压缩影射原理的稳定性分析方法，而传统基于模型控制理论与方法，或称现代控制理论与方法，其稳定性证明是利用Lyapunov稳定性理论来分析的。基于Lyapunov稳定性理论的方法，需要系统精确的数学模型，鲁棒性差。

The stability, monotonic convergence of the error dynamics, and internal stability of the MFAC schemes are proved rigorously. The stability analysis is based on the contraction mapping principle, not the Lyapunov stability theory. The contraction mapping based stability proof method is novel in the adaptive control research community, and it might be the fundamental method for control system design when the system model is unavailable.

The theoretical stability analysis for CFDL-MFAC scheme for SISO nonlinear systems is in [1，4], the PFDL-MFAC scheme is in [5], and most general FFDL-MFAC scheme is published in [6]. For MIMO cases, the stability results are in [7-8] for the different MFAC schemes.

4、先进性 [Superiority]

MFAC理论不仅具有框架性的系统体系、严谨的理论基础，同时还具有理论的先进性，主要表现在：

◆传统基于模型的现代控制理论与方法中的诸多根本理论难题，如精确建模与模型简约、未建模动力学与鲁棒性、持续激励条件与闭环控制、理论结果丰富与可实际应用算法少等在MFAC框架下都不存在。

◆理论上已经严谨证明，MFAC理论包括经典PID、线性时不变系统的自适应控制作为其特例[6]。进一步，从理论体系上讲，传统的迭代学习控制理论也可以被证明是MFAC理论在迭代轴上的特例。间接型迭代学习控制首篇文献见论文[9]。直接型的迭代学习控制见文献[10-12]。传统迭代学习控制器结构都是无模型自适应迭代学习控制的特例。另外，无模型自适应迭代学习控制系统的收敛性分析的证明都是在标准2模意义下的单调收敛，而不是传统PID型迭代学习控制收敛性证明是模意义下的单调收敛。

◆MFAC理论以及其特有的非线性系统动态线性化数据模型，已经被应用于各种控制理论分之中，且发展出若干控制理论新的研究方向，如数据驱动无模型多智能体协调/编队控制、数据驱动滑模控制、数据驱动网络控制、数据驱动预测控制、事件驱动的无模型自适应控制、数据驱动的故障诊断与自适应容错控制、数据驱动网络预测控制、无模型自适应迭代学习控制、基于观测器的数据驱动自适应控制、网络攻击下的无模型自适应控制，等等。具体参见附件2。

MFAC has not only a systematic framework with rigorous stability guarantee, but also has progressiveness and compatibility with the other control methods.

◆Since MFAC is designed by only using the measured closed-loop I/O data of the controlled plant, and the unsolvable theoretical problems in traditional model-based control theory, such as the accurate modeling and model reduction, the unmolded dynamics and robustness, the persistent excitation condition and the closed-loop control, etc., do not exist under the framework of MFAC theory owing to the fact that all the information of plant dynamics is included in the I/O measurement data.

◆The well-known PID control and the traditional adaptive control for discrete-time linear time-invariant systems can be explicitly shown as the special cases of MFAC theoretically. Further, from the view point of MFAC, the traditional iterative learning control (ILC) theory for the discrete-time nonlinear systems can be regarded as the special case of MFAC in the iteration axis due to that the traditional ILC requires a pre-specified constructive controller structure and a constant control gain for the strictly repetitive task with ideal assumptions including the identical initial values, identical desired trajectory, and affine nonlinearity. The model free adaptive iterative learning control (MFAILC) consists of indirect MFAILC [9] and direct MFAILC [10-12]. All the controller forms in traditional ILC can be shown explicitly as special cases of MFAILC controllers, which is designed with a systematic theory-supported way in both indirect and direct MFAILC. Final, the learning errors for both kinds of MFAILC schemes are guaranteed to converge monotonically to zero in the normal distance measurement with rigorously mathematics analysis rather than the lambda norm sense.

◆In additional, MFAC theory and the dynamic linearization data model methods have been used in many control theory branches to give birth to some novel data driven control methods or research directions, such as data driven model free multi-agent consensus or formation control, data driven sliding mode control, data driven networked control, data driven predictive control, event-triggered MFAC, data driven fault diagnosis and adaptive fault-tolerant control, data driven networked predictive control, observer based MFAC, MFAC under attacks, etc. See Annex 2 for details.

5、可应用性[Applicability]

  到目前为止，MFAC理论已经得到广泛的引用和应用。

◆  14部专著2部教材至少整章整节以上引用，其中包括4部国外著名出版社出版的英文专著，1部是“控制工程手册”整节引用。参见附件1。

◆ 230余个不同实际系统中得到成功应用，多数是实验室实验装置上的实际验证和真是实际系统中的应用。参见附件5。

◆ 国内外53本博士论文1整章以上的引用与应用，其中包括美国、英国、德国、瑞士、巴西、法国、罗马尼亚国外著名大学博士论文7本。258本硕士论文几乎都是应用无模型自适应控制的研究成果。见附件3。

◆ 截止到2021年6月，国内同行学者应用MFAC申请的发明专利120项。见附件4。

  Until now, MFAC has been widely applied in many practical fields and the theoretical researches:

◆ MFAC has been recorded as at least with one whole chapter or section content in 14 monographs and 2 textbooks, including 4 English monographs, and one called Control Engineering Handbook. See Annex 1 for details.

◆ MFAC has been successfully applied in more than 230 different practical plants of different physical equipment, industrial field applications or the simulation examples with physical backgrounds. See Annex 5 for details.

◆ MFAC has been directly applied or studied with more than one chapter in 53 doctoral thesis, including 7 thesis from well-known foreign universities of USA, UK, Germany, Switzerland, Brazil, France, and Romania. Total 258 master dissertations focus on the MFAC improvements or applications. See Annex 3 for details.

◆ Till June of 2021, there are 120 patents hold by others using MFAC theory as the key technology only within in China. See Annex 4 for details.

主要参考文献
[Reference]

[1]  侯忠生, 非线性系统参数辨识, 自适应控制及无模型学习自适应控制, 沈阳: 东北大学博士论文, 1994. [Z. S. Hou, The parameter identification, adaptive control and model free learning adaptive control for nonlinear systems, Ph.D. dissertation, Northeastern University, Shenyang, China, 1994.]

[2]   Zhongsheng Hou and Shangtai Jin, “Model Free Adaptive Control: Theory and Applications,” CRC Press, Taylor & Francis Group, 2013

[3]   Zhongsheng Hou and Yuanming Zhu, Controller-Dynamic-Linearization Based Model Free Adaptive Control for Discrete-Time Nonlinear Systems, IEEE Transactions on Industrial Informatics, 9(4), 2013, pp2301-2309.

[4]   Z. S. Hou and W.H. Huang, The model-free learning adaptive control of a class of SISO nonlinear systems, American Control Conference, 1997, 343-344.

[5]   Z. S. Hou and S. T. Jin, A novel data-driven control approach for a class of discrete-time nonlinear systems, IEEE Transactions on Control Systems Technology, 2011, 19(6): 1549-1558.

[6]   Z. S. Hou, and S. S. Xiong, On Model-Free Adaptive Control and its Stability Analysis，IEEE Transactions on Automatic Control, 64(11), pp4555-4569, 2019

[7]   Z. S. Hou and S. T. Jin, Data-driven model-free adaptive control for a class of MIMO nonlinear discrete-time systems, IEEE Transactions on Neural Networks, 2011, 22(12): 2173-2188.

[8]   S. S. Xiong, Z. S. Hou, Model-Free Adaptive Control for Unknown MIMO Non-affine Nonlinear Discrete-time Systems with Experimental Validation，IEEE Transactions on Neural Networks and Learning Systems，DOI: 10.1109/TNNLS.2020.3043711

[9]   Ronghu Chi, and Zhongsheng Hou, Dual-stage optimal iterative learning control for nonlinear non-affine discrete-time systems, Acta Automatica Sinica, 33 (10), 1061-1065, 208

[10]  Z. S. Hou, X. Yu, and C. K. Yin, “A data-driven iterative learning control framework based on controller dynamic linearization,” in Proceedings of the 2018 Annual American Control Conference, Milwaukee, USA, 2018, pp. 5588–5593.

[11]  Xian Yu, Zhongsheng Hou, Marios Polycarpou, and Li Duan, Data-Driven Iterative Learning Control for Nonlinear Discrete-Time MIMO Systems, IEEE Transactions on Neural Networks and Learning Systems. DOI: 10.1109/TNNLS.2020.2980588

[12]  Xian Yu, Zhongsheng Hou, Marios Polycarpou, A Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems, IEEE Transactions on Cybernetics, DOI: 10.1109/TCYB.2020.3029596

 

 

二、数据驱动迭代学习控制（DDILC）理论及应用

传统迭代学习控制（ILC）理论四类方法中：基于压缩影射原理的ILC，基于能量函数的ILC，基于模最优的ILC、以及点对点ILC，仅第一类方法属于数据驱动控制设计，后三种是基于模型的设计方法。但基于压缩影射原理的ILC，其控制器结构设计是构造性的，且控制器增益是常值，收敛性是l模意义下的单调收敛，要求初始条件和期望轨线严格重复。

DDILC基于迭代轴上的动态线性化方法进行设计，是MFAC在迭代轴上的推广，其控制器结构、控制器增益整定算法均由优化理论推导而来，不要求初始条件和期望轨线严格重复，仅利用系统I/O数据设计与分析，且具有自适应学习能力。DDILC包括间接型和直接型两类，且可严谨证明，DDILC包括传统ILC几乎所有控制器结构形式。科学意义在于传统迭代学习控制理论已经被发展成数据驱动迭代学习控制理论。

DDILC主要参考文献

[1]   卜旭辉 侯忠生，网络约束迭代学习控制理论，科学出版社，2019 [Xuhui Bu and Zhongsheng Hou, Iterative Learning Control Theory under the Networked Constraints, Science Press, 2019]

[2]    Chi Ronghu, Zhongsheng Hou, Dual stage optimal iterative learning control for nonlinear non-affine discrete-time systems, Acta Automatica Sinica, 33(10), 1061-1065. 2007

[3]    Chenkun Yin, Jian-Xin Xu, Zhongsheng Hou, A High-order Internal Model Based Iterative Learning Control Scheme for Nonlinear Systems with Time-iteration-varying Parameters, IEEE Transactions on Automatic Control, 55(11), 2665-2670, 2010

[4]    Ronghu Chi, Zhongsheng Hou, Shangtai Jin, Danwei Wang and Jiangru Jian, "Enhanced Data-driven Optimal Terminal ILC Using Current Iteration Control Knowledge", IEEE Transactions on Neural Networks and Learning Systems, 26(11), pp2939-2948, 2015

[5]   Ronghu Chi, Zhongsheng Hou, and Jianxin Xu, A discrete-time adaptive ILC for systems with iteration-varying trajectory and random initial condition, Automatica, 44,2207–2213, 2008.

[6]    Z. S. Hou, X. Yu, and C. K. Yin, A data-driven iterative learning control framework based on controller dynamic linearization, in Proceedings of the 2018 Annual American Control Conference, Milwaukee, USA, 2018, pp5588–5593.

[7]    Q Yu, Z Hou, X Bu, Q Yu, RBFNN-Based Data-Driven Predictive Iterative Learning Control for Nonaffine Nonlinear Systems, IEEE transactions on neural networks and learning systems. 31(4), 1170-1182, 2020

[8]   X. Yu, Z. S. Hou and M. Polycarpou, A Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems, IEEE Trans. on Cybernetics, DOI: 10.1109/TCYB.2020.3029596

 

 

 DDILC理论已经被成功应用于交通控制领域，包括道路交通交叉口信号灯控制、快速路交通入口匝道控制，与高速列车以及地铁列车运行控制中，实现了交通系统重复性运行模式的利用，避免了交通系统建模困难等根本难题。具体文献见https://assc.qdu.edu.cn/.

DDILC交通应用主要参考文献

[1]  Zhongsheng Hou and Jian-Xin Xu, Freeway traffic density control using iterative learning control approach, The IEEE 6th International Conference on Intelligent Transportation Systems, Shanghai, China, October 12-15, 2003

[2]  Zhongsheng Hou, Jian-Xin Xu and Hongwei Zhong, Freeway Traffic Control Using Iterative Learning Control Based Ramp Metering and Speed Signaling, IEEE Transactions on Vehicular Technology, Regular paper. 56(2), 466-477, 2007

[3]  Zhongsheng Hou and Ting Lei, Constrained Model Free Adaptive Predictive Perimeter Control and Route Guidance for Multi-Region Urban Traffic Systems, IEEE Transactions on Intelligent Transportation Systems, DOI: 10.1109/TITS.2020.3017351

[4]  Dai Li and Zhongsheng Hou, Perimeter Control of Urban Traffic Networks Based on Model-Free Adaptive Control, IEEE Trans.on Intelligent Transportation, 22(10), 2021, p6460-6472

[5]  Ye Ren, Zhongsheng Hou, Isik Ilber Sirmatel, and Nikolas Geroliminis, Data driven Model Free Adaptive Iterative Learning Perimeter Control for Large scale Urban Road networks, Transprotation Research, Part C. 115, 2020, 102618

[6]  Zhongsheng Hou and Yi Wang, Terminal Iterative Learning Control Based Station Stop Control of a Train, International Journal of Control, 84(7), 1263-1274, 2011

[7]  Heqing Sun, Zhongsheng Hou, and Dayou Li, Coordinated Iterative Learning Control Schemes for Train Trajectory Tracking with Overspeed Protection, IEEE Transactions on Automation Science and Engineering, 10(2), p323-333, 2013

[8]  Qiongxia Yu, Zhongsheng Hou and Jian-Xin Xu, D-type ILC based dynamic modeling and norm optimal ILC for high-speed trains, IEEE Transactions on Control Systems Technology, 26(2), pp652-663, 2018

 

三、数据驱动控制理论

数据驱动控制（Data Driven Control）作为学术集合名词首次在文献[1-3]给出，自提出以来受到普遍承认，并受邀写入IFAC战略发展白皮书中[4]。数据驱动控制作为一个控制理论的学科分支除包括上述具体数据驱动控制方法外，最近几年还出现了一些新数据驱动方法，如文献[5-6]。

[1]    侯忠生 许建新, 数据驱动控制理论及方法的回顾和展望，自动化学报，35(6)，pp650-667, 2009.

[2]    Zhongsheng Hou and Zhuo Wang，From Model Based Control to Data Driven Control: Survey, Classification and Perspective, Information Sciences, 235(20), pp3-35, 2013.

[3]   Zhongsheng Hou, Ronghu Chi and Huijun Gao, An Overview of Dynamic-Linearization-Based Data-driven Control and Applications, IEEE Transactions on Industrial Electrnoics, vol. 64, no. 5, pp. 4076–4090, 2017.

[4]   Francoise Lamnabhi-Lagarrigue, Anuradha Annaswamy, Sebastian Engell, Alf Isaksson, Pramod Khargonekar, Richard M. Murray, Henk Nijmeijer, Tariq Samad, Dawn Tilbury, Paul Van den Hof, “Systems & Control for the future of humanity, research agenda: Current and future roles, impact and grand challenges,” Annual Reviews in Control, 43, pp1–64, 2017. Section 4.2 [By Zhongsheng Hou].

[5]   Yongqiang Li and Zhongsheng Hou, Data-Driven Asymptotic Stabilization for Discrete-Time Nonlinear Systems, Systems &Control Letter, 64, 79-85, 2014

[6]   Yongqiang Li, Zhongsheng Hou, Yuanjing Feng* and Ronghu Chi, Data-Driven Approximate Value Iteration with Analysis of Optimality Error Bound, Automatica, 78, p79-87, 2017