Development Forum 1: Modeling, Identification, Analysis and Control of Stochastic Systems
Author:张虎山  Time:2022-06-13   Views:14

发展论坛 (Development Forums)

Development Forum 1


 72613:30-15:30

 July 26, 13:30-15:30


  

Modeling, Identification, Analysis and Control of Stochastic Systems

随机系统的建模、辨识、分析与控制

                   Chairs: Zidong Wang (Brunel University London, U.K.)

                   Feiqi Deng (South China University of Technology, China)


Panelists: George Yin (University of Connecticut, USA)

  Zhan Shu (University of Alberta, Canada)

  Jianglun Wu (Swansea University, UK)

  Wenxiao Zhao (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China)

  Jun Hu (Harbin University of Science and Technology, China)

 

Abstract: Generally, randomness causes difficulties for the analysis and design of systems, while it may bring about excitations to us, for example the stabilization of systems by noise, thus the theory of stochastic systems is challenging, practical and also interesting. In recent years, the analysis and synthesis problems of stochastic systems have received a great deal of attention from researchers in applied mathematics and control engineering. Especially, the applications of the stochastic system to the networked control and swarm intelligence systems become hot topics in the recent years. In this forum, five experts from USA, Canada, UK and China have been invited to give their talks on the topics of Modeling, Identification, Analysis and Control of Stochastic Systems, with intention to share their latest research progress with the interested audience.

 

Title: Stochastic Kolmogorov Systems and Applications

Abstract: The talk reports some of our joint work with D.H. Nguyen and N.N Nguyen, and also the work with N.T. Dieu, N.H. Du, among others. In the talk, we present some of our recent work on stochastic Kolmogorov systems. The motivation stems from dealing with important issues of ecological and biological systems. Focusing on environmental noise, we aim to address such fundamental questions as what are the minimal conditions for long-term persistence of a population, or long-term coexistence of interacting species.

George Yin received the B.S. degree in mathematics from the University of Delaware in 1983, and the M.S. degree in electrical engineering and the Ph.D. degree in applied mathematics from Brown University in 1987. He joined Wayne State University in 1987, became Professor in 1996, and University Distinguished Professor in 2017.

He moved to the University of Connecticut in 2020. His research interests include applied probability, stochastic processes, and stochastic systems theory and applications. He served as Co-chair for a number of conferences and served on many committees for IEEE, IFAC, and SIAM. He was Chair of the SIAM Activity Group on Control and Systems Theory, and was on the Board of Directors of the American Automatic Control Council. He is Editor-in-Chief of SIAM Journal on Control and Optimization, Associated Editor of Applied Mathematics and Optimization, ESAIM: Control, Optimisation and Calculus of Variations, and on the editorial boards of many other journals. He was an Associate Editor of Automatica 1995-2011, IEEE Transactions on Automatic Control 1994-1998, and Senior Editor of IEEE Control Systems Letters 2017-2019. He is a Fellow of IEEE, a Fellow of IFAC, and a Fellow of SIAM.

 

TitleEvent-Triggered Robust Model Predictive Control with Stochastic Event Verification

Abstract: In this talk, a new type of event-triggered MPC control approach is introduced. Based on the ergodicity of a purposely designed Markov chain, a stochastic triggering scheme involving a prescribed triggering function, an updating law for the transition probabilities of the Markov chain, and a checking function is proposed to achieve aperiodic and non-persistent event verification and enlarge the inter-execution time. Both tube-based MPC and linear matrix inequality-based (LMI-based) MPC are considered, and they show complementary merits with such a stochastic triggering scheme. Under mild conditions, recursive feasibility and closed-loop robust stability of both approaches are guaranteed theoretically. When the disturbance is generated by a Gaussian white-noise random process, the relation between the average performance cost and inter-execution time is explored analytically. Simulation results are provided to show the effectiveness and merits of the proposed approaches.

Zhan Shu received his B.Eng. degree in Automation from Huazhong University of Science and Technology in 2003, and his Ph.D. degree in Control Engineering from The University of Hong Kong in 2008. For his doctoral research, he received the award for Outstanding Research Postgraduate Student of the University of Hong Kong. He was a Post-Doctoral Fellow in the Hamilton Institute, National University of Ireland, Maynooth, from 2009 to 2011, and a Lecturer in the Faculty of Engineering and Physical Sciences, the University of Southampton from 2011 to 2019. Since 2020, he has been a faculty member at the Department of Electrical and Computer Engineering, University of Alberta, where he is currently an Associate Professor. He is a Senior Member of IEEE, a Member of IET, and an invited reviewer of the Mathematical Review of the American Mathematical Society. In addition, he serves as an Associate Editor for a couple of journals and conferences, e.g., IEEE Transactions on Automatic Control, and the IEEE Control Systems Society Conference Editorial Board.

 

Title: Characterising the Path-independence of Stochastic Differential Equations

Abstract: This talk will address a problem arising in financial modelling with stochastic differential equations (SDEs). A characterisation theorem will be derived in which we establish a new link from SDEs to nonlinear parabolic PDEs. Starting from the necessary and sufficient conditions of the path-independence of the density of Girsanov transform for SDEs, we are able to derive a characterisation by means of nonlinear parabolic equations of Burgers-KPZ type. The obtained result reveals the feature of state dependence of certain additional functions of stochastic systems governed by SDEs. Extensions to the cases of degenerated SDEs, jump SDEs, DDSDEs, as well as to (infinite dimensional) SDEs on separable Hilbert spaces will be discussed. 

Jiang-Lun Wu is a professor of mathematics at Swansea University, UK. He is a member of London Mathematical Society. He obtained his Ph. D degree in Probability and Mathematical Statistics from the Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, under the supervision of Academician Jia-An Yan. Before join Swansea University at 2001, he was Alexander von Humboldt research fellow and then Assistant at Ruhr-University Bochum, Germany, and research fellow at the Institute of Applied Mathematics, University of Bonn, Germany. His main area of interest is probability theory and stochastic analysis, focusing on the analysis of stochastic partial differential equations arising from mathematical and statistical physics. He is also interested in modelling and simulations of stochastic processes linked with data analytics in economics and finance, as well as in biology. He has published more than 110 papers in journals including Annals of Applied  Probability, Journal of Functional Analysis, Journal of Differential Equations, Transactions of the American Mathematical Society, Stochastic Processes and their  Applications, Potential Analysis, Bulletin des Sciences Mathématiques, Communications in Mathematical Physics, and so on. 

 

Title: A General Framework for Nonparametric Identification of Nonlinear Stochastic Systems

Abstract: In this talk, nonparametric identification of nonlinear autoregressive systems with exogenous inputs (NARX) is considered; a general criterion function is introduced for estimating the value of the nonlinear function within the system at any fixed point. The criterion function is constructed using a kernel together with a convex objective function. Not only does this framework include the classical kernel-based weighted least-squares estimator but also the kernel-based Ll, l>=1 criteria as special cases. First, we prove that the minimizer of the general criterion function converges to the true function value with probability 1. Second, recursive algorithms are proposed to find the estimates, which minimize the criterion function, and it is shown that these estimates also converge to the true function value with probability 1. Numerical examples are given, justifying that the framework guarantees the strong consistency of the estimates and exhibits the robustness against outliers in the observations.

Wenxiao Zhao received the B.Sc. degree from Shandong University, Jinan, China, in 2003 and the Ph.D. degree in operation research and cybernetics from the Institute of Systems Science (ISS), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS), Beijing, China, in 2008. He is a Professor with AMSS, CAS. His research interests include mainly in machine learning, system identification, and adaptive control as well as distributed stochastic optimization.

 

 

Title: Design and Evaluation of Optimized State Estimation Algorithm for Stochastic Time-varying Complex Networks

Abstract: Over the past years, the investigation of the complex networks has become an emerging research topic due to its strong advantages on modelling/analyzing the practical systems, such as biological networks, power grid, traffic networks and technological networks. In this talk, we mainly focus on the design and evaluation problems of optimized state estimation algorithm for stochastic time-varying complex networks, where the influences from the missing measurements, randomly switching topologies and dynamical bias onto the estimation performance are discussed. Firstly, the detailed formulations with respect to those phenomena are given. Next, the time-varying state estimators with compensation ability are designed, moreover, the corresponding optimized state estimation algorithms with expression forms of the estimator gains are proposed. Furthermore, the performance analysis problems of the state estimation algorithm are examined. Finally, some simulation experiments are provided to illustrate the validity and advantages of the main results.

 

Jun Hu is a Professor and Dean of School of Automation, Harbin University of Science and Technology. He received Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology in 2013. He is the receipt of the Alexander von Humboldt fellow in 2014. His research interests include nonlinear control, filtering and fault estimation, time-varying systems and complex networks. He has published 1 English monograph and more than 80 papers in refereed international journals. He serves as a reviewer for Mathematical Reviews, as an editor for Neurocomputing, Neural Processing Letters, Systems Science and Control Engineering, and as a guest editor for International Journal of General Systems and Information Fusion.