Keynote Speakers

Yury Kochetov, Bilevel mathematical models for economic competition

Evgeny Spodarev, Prediction of Heavy-Tailed Random Functions

Jajati Keshari Sahoo, Matrix splitting based iterative schemes for large linear systems

Shuai Li, BAS-An Emerging Global Optimization Tool for Real-time Light-weighted AI

Long Jin, Neural Dynamics Based Learning and Control of Robots

Ivana Micic, The concept of approximate regular fuzzy relation and its applications

Stefan Stanimirovic, Towards new equivalence modelling for fuzzy automata

Lin Xiao, A Novel Predefined-Time ZNN Model for Time-Dependent Matrix Inversion

Bilevel mathematical models for economic competition

Bilevel optimisation is an important class of hierarchical optimisation problems with two decision-makers: the leader and the follower. The leader cannot control the follower’s decisions but can change his constraints and the objective function. The goal or profit of the leader depends on the optimal decision of the follower. Over the last 30 years, the bilevel problems have received significant attention from the mathematical programming and operational research communities. This talk provides an overview of bilevel discrete optimisation including basic definitions, properties, relationships to other classes of optimisation problems and applications. We aim to encourage researchers to pay more attention to this interesting area both from the theoretical point of view and applications.

Prediction of Heavy-Tailed Random Functions

Joint work with Abhinav Das and Vitaly Makogin

Kriging methods are classically used for the extrapolation of square integrable random fields. For heavy tailed random processes and fields, this theory cannot be applied.

We fill this gap and construct a unified approach for the extrapolation of stationary (possibly heavy tailed) random functions using the comparison of their level sets.

For that, a new excursion metric for random variables is defined, and its properties are studied. Then it is shown how the new metric is connected to the error-in-measure of level sets of the process and it predictor. For the case of Gaussian processes and linear prediction, the new metric is minimised subject to the constraint that the predictor has the same marginal distribution as the original process. Properties of the new prediction such as consistency and exactness are studied. In the Gaussian case, the existence and uniqueness of the solution of the corresponding linear programming problem with quadratic constraints are analysed. Numerical examples round up the talk.

Matrix splitting based iterative schemes for large linear systems

The linear or singular systems are arising in various branch of Science and Engineering such as statistical models, forecast modelling and partial differential equations. Several iterative methods are proposed for singular system to improve the convergence rate as well better complexity. In this talk, we will discuss alternating iterative schemes based on some splittings and generalized inverses. In addition to these, we will explain a few other approaches such as regularization theory and pre-conditioning techniques to relax some conditions. At the end, an application to Poisson problem will be illustrated.

BAS-An Emerging Global Optimization Tool for Real-time Light-weighted AI

Beetle Antennae Search (BAS) since its invention in 2018 has been widely used in addressing various online optimization problems due to its unique features of low computational burden, ability of global optimization, model free, fast computation, low amount of code, etc. As an alterative to genetic algorithms and particle swarm optimization, BAS can be easily deployed in embedded microcontrollers. This talk will give an introduction to the basic principles of BAS and its application in various engineering practice.

Neural Dynamics Based Learning and Control of Robots

The existing research has achieved success in learning and control of robots by using intelligent algorithms. However, most solutions require a large amount of data for network training, and there are some weaknesses, such as weak robustness and slow learning rates. To explore effective learning approaches, we establish a neural-dynamics-based unified framework for the learning and control of robots. Specifically, several synchronous learning and control strategies and corresponding neural dynamics are proposed for complex robot systems, such as multi-robot systems, robot visual servoing systems, mobile robot systems, and robot motion and force control systems. These research technologies include neural dynamics, data-driven technology, Kalman filtering algorithm, and robot technology. Abundant simulations, robotic experiments, and comparisons are carried out, and the results substantiate the robustness, practicability, and superiority of the proposed schemes when encountering uncertain situations.

The concept of approximate regular fuzzy relation and its applications

Analysis of a large amount of data that occur in real-life systems, such as fuzzy social networks, is almost impossible without prior factorization of the observed network by its specific properties. For this purpose, scientists have developed different methods for factorization of such networks, and some of them use the so-called regular fuzzy relations. Here, we introduce new types of regular fuzzy relations that generalize previously defined ones. They are called mu-approximate regular fuzzy relations, where mu presents the degree to which the original and the factorized fuzzy network (obtained by using these fuzzy relations) are equivalent. These new fuzzy relations perform excellently in the factorization of fuzzy networks. Specifically, by using mu-approximate regular fuzzy relations, we show that it is possible to reduce a fuzzy social network in some cases when previously developed algorithms fail to reduce it. We examine the properties of approximate regular fuzzy relations and propose the procedure for calculating the greatest approximate regular fuzzy relation on a given fuzzy social network. For fuzzy social networks defined over the real-unit interval [0, 1], we give a method that computes all subintervals of [0, 1] that share the same greatest approximate regular fuzzy relation.

Towards new equivalence modelling for fuzzy automata

Real-life systems have been modelled via various mathematical notions. For a chosen mathematical notion, it happens frequently that multiple models exist for the observed system. Numerous techniques have been developed to determine the equivalence of these models. When real-life systems are modelled by fuzzy automata, one very convenient way to check the equivalence is to use the well-established notion of bisimulation, which intuitively allows us to group fuzzy automata by the way they match each other’s moves. In other words, the notion of bisimulation allows us to model the indiscernibility of states of fuzzy automata.

In this talk, we shed a light on the so-called approximate bisimulations for fuzzy automata. They have the property that, if there exists an approximate bisimulation between two fuzzy automata, then they are equivalent to some degree (i.e., each input word is recognized by the fuzzy automata in degrees that differ up to the chosen limit). Their main advantage is that there may not exist a bisimulations between two fuzzy automata, but there may exist an approximate bisimulation, while the language equivalence for fuzzy automata is preserved up to a high degree. We examine further properties of approximate bisimulations, and on the ways that they group equivalent fuzzy automata.

A Novel Predefined-Time ZNN Model for Time-Dependent Matrix Inversion

The problem of solving complex-valued time dependent matrix inversion (CDTV-MI) has significant implications for statistics and control theory, and thus it is worthy to be investigated by scholars. Zeroing neural network (ZNN) is an efficient tool for solving time-dependent problems and can be used to get the inverse of complex-variable matrix in disturbed environments. In this paper, a complex-valued fast predefined zeroing neural network (CFPZNN) model is proposed for solving the CDTV-MI problem. The CFPZNN model possesses two considerable properties. In the first place, the predefined time convergence performance ensures that the CFPZNN model can solve the CDTV-MI problems efficiently. In the second place, the CFPZNN model has suprior robustness and can restrain the interference of noise. These two superior points are demonstrated through several sets of numerical simulations. Moreover, the effectiveness and advantages of the proposed CFPZNN model are further demonstrated by citing the widely applied activation functions for comparison.