Ivan Ivanov

• Doctor Science
• Professor at Sofia University "St. Kliment Ohridski"

This study demonstrates the complexity and importance of water quality as a measure of the health and sustainability of ecosystems that directly influence biodiversity, human health, and the world economy. The predictability of water quality thus plays a crucial role in managing our ecosystems to make informed decisions and, hence, proper environme...

This paper presents both sufficient and necessary conditions for polyhedral sets and symmetric polyhedral sets to be robust positively invariant sets within perturbed linear discrete-time systems. These conditions are derived through the application of optimization and dual optimization theory. By leveraging the definition of a robust positively in...

This study meticulously explores the crucial elements precipitating corporate failures in Taiwan during the decade from 1999 to 2009. It proposes a new methodology, combining ANOVA and tuning the parameters of the classification so that its functional form describes the data best. Our analysis reveals the ten paramount factors, including Return on...

Diabetes causes an increase in the level of blood sugar, which leads to damage to various parts of the human body. Diabetes data are used not only for providing a deeper understanding of the treatment mechanisms but also for predicting the probability that one might become sick. This paper proposes a novel methodology to perform classification in t...

The presented methodology provides an innovative way to answer a question that is rarely observed in academic literature: How can complex data issues like multiple class imbalance be solved using the available models in a simple and efficient way? In this approach, observations are modeled without additional preprocessing. Several classification mo...

This paper studies the estimation of reachable sets for discrete-time singular systems with time-varying delays and bounded peak inputs. A novel linear matrix inequality condition for the reachable set estimation of the time-varying time-delay discrete singular system is derived using an inverse convex combination and the discrete form of the Wirti...

Stroke prediction is a vital research area due to its significant implications for public health. This comparative study offers a detailed evaluation of algorithmic methodologies and outcomes from three recent prominent studies on stroke prediction. Ivanov et al. tackled issues of imbalanced datasets and algorithmic bias using deep learning techniq...

We consider a linear quadratic differential game on an infinite time horizon with two types of an information structure. The game models are considered in both information structures: the open loop design and feedback design. The Newton solver for computing the stabilizing solution of the associated Nash-Riccati equations has been established. More...

In this paper, we investigate a Lyapunov trajectory tracking design method that incorporates a Schrödinger equation with a dipole subterm and polarizability. Our findings suggest that the proposed control law can overcome the limitations of certain existing control laws that do not converge. By integrating a quadratic performance index, we introduc...

This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant set for these systems by tackling the dual problem associated with semidefinite programming. Central...

This paper investigates a quantum system described by the Schrödinger equation, utilizing the concept of the quantum Lyapunov function. The Lyapunov function is chosen based on the mean value of a virtual mechanical quantity, where different values of P, the mean value of the virtual mechanical quantity in the Lyapunov function, have an impact on t...

This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on th...

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we conside...

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control system with bounded disturbances. First, by constructing an appropriate Lyapunov-Krasovskii functional, we obtained a delay-dependent condition, which determed the admissible bounding ellipsoid for the reachable set of the system we c...

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control system with bounded disturbances. First, by constructing an appropriate Lyapunov-Krasovskii functional, we obtained a delay-dependent condition, which determed the admissible bounding ellipsoid for the reachable set of the system we c...

In this paper, we investigate the iterative methods for the solution of different types of nonlinear matrix equations. More specifically, we consider iterative methods for the minimal nonnegative solution of a set of Riccati equations, a nonnegative solution of a quadratic matrix equation, and the maximal positive definite solution of the equation...

Stroke is a major public health issue with significant economic consequences. This study aims to enhance stroke prediction by addressing imbalanced datasets and algorithmic bias. Our research focuses on accurately and precisely detecting stroke possibility to aid prevention. We tackle the overlooked aspect of imbalanced datasets in the healthcare l...

This paper proposes two novel methods for computing the robustly controlled invariant set of linear discrete-time systems with additive bounded disturbances. In the proposed methods, the robustly controlled invariant set of discrete-time systems is obtained by solving the linear matrix inequality given by logarithmic norm and difference inequality....

A positively invariant set is an important concept in dynamical systems. The study of positively invariant set conditions for discrete-time systems is one interesting topic in both theoretical studies and practical applications research. Different methods for characterizing the invariance of different types of sets have been established. For exampl...

Consider an iterative modification of the linearized Newton method for computing the minimal nonnegative solution of a a nonsymmetric Nash-Riccati equation. The equation has arisen in linear quadratic games for positive systems. The Newton procedure for computing the minimal nonnegative solution is well known in the the literature. Our proposal is...

This study's objective is to offer a practical computer method for handling classification problems on large datasets. The aim of this study is to offer a practical computer approach for handling classification tasks on big datasets. We show that using Python’s built-in parameters to balance classes can improve the accuracy and the metrics of a cla...

Positive invariant set is an important concept of dynamic systems. The purpose of this paper is to study the sufficient and necessary conditions that the set of ellipsoids and the Lorenz cone are positive invariant sets of discrete time systems. By means of nonlinear programming and induced norm, the problem of positive invariance is formulated as...

Horadam sequence is a general recurrence of second order in the complex plane, depending on four complex parameters (two initial values and two recurrence coefficients). These sequences have been investigated over more than 60 years, but new properties and applications are still being discovered. Small parameter variations may dramatically impact t...

In this research we summarize how machine learning algorithms can be used for decision making that can affect health policies. We present modified ANOVA algorithm for identifying marker leukemia genes that allows deeper examination of genes subsets that can increase the risk of developing leukemia. The algorithm uses the ANOVA, the bootstrap and cl...

In this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them wants to minimize the deviation of a preferential output of the controlled...

We investigate a linear quadratic tracking problem for impulsive controlled stochastic systems. The main tool in the derivation of the optimal control is the stabilizing solution for a class of backward jump matrix linear differential equation. We introduce the concept of mean square stability by impulses and consider the properties of stabilizing...

"We investigate a problem to solve the linear quadratic tracking problem for stochastic systems controlled by impulses. Two optimal control problems are investigated where the different objective functions are minimized. Explicit formulae for optimal controls are developed. The optimal controllers are computed based on the solution of the backward...

In this paper, we examine a sampled-data Nash equilibrium strategy for a stochastic linear quadratic (LQ) differential game, in which admissible strategies are assumed to be constant on the interval between consecutive measurements. Our solution first involves transforming the problem into a linear stochastic system with finite jumps. This allows u...

Hepatitis C can be a life threatening condition, whose severity depends on the stage of development. The stage of development of hepatitis C determines the chances of survival. In recent years machine learning algorithms have focused on predicting the stage of hepatitis development. The dataset called HCV is often used in machine learning experimen...

In this paper we consider the problem of minimization of the mean square value of the deviation of a random signal z(tf ) from a given target ζ. The random signal z(tf ) represents the value at instant time tf of an output of a controlled dynamical system described by an Itˆo differential equation. Both the case when the set of admissible controls...

In this paper we consider the problem of minimization of the mean square value of the deviation of a random signal z(tf ) from a given target ζ. The random signal z(tf ) represents the value at instant time tf of an output of a controlled dynamical system described by an Itˆo differential equation. Both the case when the set of admissible controls...

In classification problems, cross-validation chooses random samples from the dataset in order to improve the ability of the model to classify properly new observations in the respective class. Research articles from various fields show that when applied to regression problems, the bootstrap can improve either the prediction ability of the model or...

The purpose of this paper is to examine the causality between DUST, CO2 and temperature for the Vostok ice core data series [Vostok Data Series], dating from 420 000 years ago, and the EPICA C Dome data going back 800 000 years. In addition, the time-varying volatility and coefficient of variation in the CO2, dust and temperature is examined, as we...

The purpose of this paper is to examine the causality between DUST, CO2 and temperature for the Vostok ice core data series [Vostok Data Series], dating from 420 000 years ago, and the EPICA C Dome data going back 800 000 years. In addition, the time-varying volatility and coefficient of variation in the CO2, dust and temperature is examined, as we...

The problem of the existence of a Nash equilibrium strategy in a state feedback form is discussed for a class of stochastic linear quadratic two players differential games. It is assumed that only measurements at discrete-time instances of the state parameters are available. Both piecewise continuous admissible strategies as well as piecewise const...

Constrained Regulation Problem (CRP) for fractional-order nonlinear continuous-time systems is investigated in this paper. New existence condition of linear feedback control law for a class of fractional-order nonlinear continuous-time systems under constraints is proposed. Computation method for solving CRP of fractional-order nonlinear systems co...

Cross validation is often used to split input data into training and test set in Support vector machines. The two most commonly used cross validation versions are the tenfold and leave-one-out cross validation. Another commonly used resampling method is the random test/train split. The advantage of these methods is that they avoid overfitting in the...

The problem of the existence of a Nash equilibrium strategy in a state feedback form is discussed for a class of stochastic linear quadratic two players differential games. It is assumed that only measurements at discrete-time instances of the state parameters are available. Both piecewise continuous admissible strategies as well as piecewise const...

We investigate a set of nonlinear matrix equations with nonnegative matrix coefficients which has arisen in applied sciences. There are papers where the minimal nonnegative solution of the set of nonlinear matrix equations is computed applying the different procedures. The alternate linear implicit method and its modifications have intensively inve...

The problem of sampled-data Nash equilibrium strategy in a state feedback setting for a stochastic linear quadratic differential game is addressed. It is assumed that the admissible strategies are constant on the interval between two measurements. The original problem is converted into an equivalent one for a linear stochastic system with finite ju...

Feature selection is a powerful tool to identify the important characteristics of data for prediction. Feature selection, therefore, can be a tool for avoiding overfitting, improving prediction accuracy and reducing execution time. The applications of feature selection procedures are particularly important in Support vector machines, which is used...

The problem to classify big data is an actual one the subject. There are multiple ways to classify data but the k Nearest Neighbors (k-NN) has become a popular tool for the data scientist. In this paper we examine several modifications of the k Nearest Neighbors algorithm that achieve better efficiency in terms of accuracy and CPU time when classif...

A linear quadratic optimal control problem for a system described by Itô differential equations with state and control dependent white noise under the assumption that the set of admissible controls consists of a class of piecewise constant stochastic processes is considered. The considered LQ optimal control problem is converted into a LQ optimizat...

In this paper, based on Kou’s classical iterative methods with fifth-order of convergence, we propose new interval iterative methods for computing a real root of the nonlinear scalar equations. Some numerical experiments have executed with the program INTLAB in order to confirm the theoretical results. The computational results have described and c...

We consider a two players linear quadratic differential game associated to a positive theta-periodic dynamical system with jump Markov perturbations. We introduce the concept of stabilizing solution and strong stabilizing solution of the associated system of coupled matrix Riccati differential equations and we will point out the relation between th...

The infinite horizon linear quadratic differential games for positive linear systems with Markovian jumping is considered. The authors' goal is to propose a set of sufficient conditions that guarantee the existence of the stabilising solution of a system of game theoretic algebraic Riccati type equations associated to the considered differential ga...

We consider a two players linear quadratic differential game associated to a positive θ-periodic dynamical system with jump Markov perturbations. We introduce the concept of stabilizing solution and strong stabilizing solution of the associated system of coupled matrix Riccati differential equations and we will point out the relation between these...

We consider a generalized algebraic Riccati equation arising in stochastic control with an indefinite quadratic part. Three effective methods for computing a matrix sequence, which converges to the stabilizing solution of the considered type of Riccati equations with indefinite quadratic parts are explored. Convergence properties of these methods a...

We investigate the problem for solving a discrete-time periodic generalized Riccati equation with an indefinite sign of the quadratic term. A necessary condition for the existence of bounded and stabilizing solution of the discrete-time Riccati equation with an indefinite quadratic term is derived. The stabilizing solution is positive semidefinite...

We consider the linear quadratic differential games for positive linear systems with the feedback information structure in the general case. Recently, several iterative methods to obtain the stabilizing solution of a corresponding set of Riccati equations are described in the literature - the Newton method and its accelerated modi cation and the Ly...

A PhD class of lectures will be jointly developed on the topic of Linear Quadratic Differential Games and Applications. The class is intended to support the learning process of the PhD students as well as to increase their competencies through acquaintance with the latest advances in the field. The total study load is planned to amount to 30 lectur...

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is...

The present paper develops an optimal linear quadratic boundary controller for 2×2 linear hyperbolic partial differential equations (PDEs) with actuation on only one end of the domain. First-order necessary conditions for optimality is derived via weak variations and an optimal controller in state-feedback form is presented. The linear quadratic re...

The present paper develops an optimal linear quadratic boundary controller for $2\times2$ linear hyperbolic partial differential equations (PDEs) with actuation on only one end of the domain. First-order necessary conditions for optimality is derived via weak variations and an optimal controller in state-feedback form is presented. The linear quadr...

This paper addresses the problem of solving discrete-time H ∞ control problems for periodic systems. The approach for solving such a type of equations is well known in the literature. However, the focus of our research is set on the numerical computation of the stabilizing solution. In particular, two effective methods for practical realization of...

This study investigates the influence of the 2008 financial crisis on a number of European stock markets. The sample includes EU benchmark indices as well as European markets with slowed or hampered recovery over a period of ten years (2004-2014) thus allowing a comparison on their development before, during and after the crisis. We utilize a novel...

This paper addresses the problem of solving a generalized algebraic Riccati equation with an indefinite sign of its quadratic term. We extend the approach introduced by Lanzon, Feng, Anderson and Rotkowitz (2008) for solving similar Riccati equations. We numerically investigate two types of iterative methods for computing the stabilizing solution....

This paper demonstrates the utilization of wavelet-based tools for the analysis and prediction of financial time series exhibiting strong long-range dependence (LRD). Commonly emerging markets' stock returns are characterized by LRD. Therefore, we track the LRD evolvement for the return series of six Southeast European stock indices through the app...

We consider a discrete-time periodic generalized Riccati equation. We investigate a few iterative methods for computing the stabilizing solution. The first method is the Kleinman algorithm which is a special case of the classical Newton-Kantorovich procedure, the second one is a method of consistent iterations and two new Stein iterations. The prop...

In the paper the infinite-horizon Linear Quadratic Regulator (LQR) problem of linear discrete time systems with non-negative state constraints is presented. Such kind of constraints on the system determine the class of positive systems. They have big application in many fields like economics, biology, ecology, ICT and others. The standard infinite...

This paper addresses the problem for solving a Continuous-time Riccati equation with an indefinite sign of the quadratic term. Such an equation is closely related to the so called full information H∞ control of linear time-invariant system with external disturbance. Recently, a simultaneous policy update algorithm (SPUA) for solving H∞ control prob...

Adaptive and relative market efficiency of seven Southeast European stock exchanges is investigated for a period of 11 years. A wavelet-based technique is utilized to the daily return series of the major stock indices in order to track the evolution of the LRD parameter, since its value is closely related to the degree of returns predictability. A...

In [1], the authors provided some comments on the paper [3]. In this note, we will address the points raised.

This paper is concerned with two kinds algebraic Riccati equations arising in the linear quadratic (LQ) control. The problem gives rise to the existence of a so-called stabilizing solution to a stochastic (generalized) algebraic Riccati equation, which is however fundamentally different from the classical algebraic Riccati equation as a result fro...

SUMMARY This paper addresses the problem of solving a class of periodic discrete-time Riccati equation with an indefinite sign of its quadratic term. Such an equation is closely related to the so-called full-information H ∞ control of discrete-time periodic systems. A globally convergent iterative algorithm with a local quadratic convergence rate i...

We consider a set of discrete-time generalized Riccati equations that arise in quadratic optimal control of discrete-time stochastic systems subjected to both state-dependent noise and Markovian jumps. The iterative method to compute the maximal and stabilizing solution of wide class of discrete-time nonlinear equations is derived by Dragan et al....

This paper addresses the problem of solving a class of periodic discrete-time Riccati equation with an indefinite sign of it's quadratic term. More precisely, we focus on the computation of the stabilizing solutions of discrete-time game theoretic periodic Riccati equations. A convergent iterative algorithm is proposed for this purpose.

The optimal control problems for positive systems is an important and extensively studied topic in recent years. In this paper, the infinite horizon LQR problem of positive linear discrete time systems (PLDS) is studied. For solving the problem we consider the approach based on the admissibility of the solution of the standard infinite discrete LQR...

Stochastic linear systems subjected both to Markov jumps and to multiplicative white noise are considered. In order to stabilize such type of stochastic systems, the so-called set of generalized discrete-time algebraic Riccati equations has to be solved. The LMI approach for computing the stabilizing symmetric solution (which is in fact the equilib...

The authors investigate the numerical solution of a set of discrete-time generalised Riccati equations. The class of discrete-time non-linear equations involves in various control problems for discrete-time stochastic systems and it can be considered as an important tool for solving optimisation control for such type systems. A new procedure for co...

The presence of stock market efficiency is a distinctive characteristic of the effectively functioning market economy. Investigation of the market efficiency of seven emerging East-European stock exchanges is carried out as their major stock indices (BELEX15, BET, CROBEX, ISE100, PFTS, RTSI, SOFIX) are studied in respect of long-range dependence (L...

We consider a set of discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control of Markovian jump linear systems. The LMI approach for computing the maximal symmetric solution of this system is studied. The special case of the Riccati equations with applications to financial modeling is commented. We construct two new...

The current paper investigates the major index of the Bulgarian Stock Exchange with respect to the presence of long-range dependence and principal predictability of the index. The wavelet transform is utilized in order to carry out the investigation since it is a well-suited tool for the analysis of fractal processes and sheds additional light to t...

This paper examines the problem of measuring sustainable governance in the European Union (EU-27) through the use of duality and the Slutsky equation. The proposed methodology is based on the application of a three-dimensional optimisation model, where the arguments of the objective (sustainable social welfare) function are economic goods that cont...

In this paper, the problem of the numerical computation of the stabilizing solution of the game theoretic algebraic Riccati equation is investigated. The Riccati equation under consideration occurs in connection with the solution of the H  ∞  control problem for a class of stochastic systems affected by state dependent and control dependent white n...

In this article, the problem of the numerical computation of the stabilising solution of the game theoretic algebraic Riccati equation is investigated. The Riccati equation under consideration occurs in connection with the solution of the H ∞ control problem for a class of stochastic systems affected by state-dependent and control-dependent white n...

This paper discusses the numerical solution of the coupled algebraic Riccati equations associated with the linear quadratic differential games. The Lyapunov iteration for solving the considered coupled equations is discussed by Li and Gajic (1994). We modify this iteration and derive the new algorithm with typically convergence properties for metho...

In this paper, the stochastic Nash games for weakly coupled large-scale systems with state-dependent noise are considered. The considered stochastic algebraic Riccati equations is quite different from the existing results in the sense that the equations have the additional linear term. The numerical algorithm based on Lyapunov iterations for solvin...

We consider a set of discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control of Markovian jump linear systems. Two iterations for computing a symmetric (maximal) solution of this system are investigated. We construct sequences of the solutions of the decoupled Stein equations and show that these sequences converge...

We consider a new type nonlinear matrix equation. We investigate the existence a positive definite solution and two iterative methods for computing this solution. The first method is the classical Newton procedure and the second is a new Stein iteration. In this paper it is proved that a new Stein iteration has convergence properties to those of th...

We consider a set of discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control. Two iterations for computing a symmetric solution of this system are investigated. New iterations are based on the properties of a Stein equation. It is necessary to solve a Stein equation at each step of proposed algorithms. We adapt the...

We consider different iterative methods for computing Hermitian solutions of the coupled Riccati equations of the optimal control problem for jump linear systems. We have constructed a sequence of perturbed Lyapunov algebraic equations whose solutions define matrix sequences with special properties proved under proper initial conditions. Several nu...

We consider the numerical solution of a set of discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control. Several iterations for computing a symmetric solution of this system are investigated and compared. New iterations are based on the properties of a Stein equation. It is necessary to solve a Stein equation at eac...

We consider different iterative methods for computing a Hermitian or maximal Hermitian solution of two types of rational Riccati equations arising in stochastic control. The classical Newton procedure and its modification applied to equations are very expensive. New less expensive iterations for these equations are introduced and some convergence p...