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The averaging method combined with the Lyapunov-Schmidt reduction provides sufficient conditions for the existence of periodic solutions of the following class of perturbative $T$-periodic nonautonomous differential equations…
A new approach to the steady state detection in the uniformization method of solving continuous time Markov chains is introduced. The method is particularly useful in solving inhomogenous CTMC's in multiple steps, where the desired error…
Astrophysical discs which are sufficiently massive and cool are linearly unstable to the formation of axisymmetric structures. In practice, linearly stable discs of surface density slightly below the threshold needed for this instability…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global…
To make research of chaos more friendly with discrete equations, we introduce the concept of an unpredictable sequence as a specific unpredictable function on the set of integers. It is convenient to be verified as a solution of a discrete…
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
Control-based continuation (CBC) is a general and systematic method to explore the dynamic response of a physical system and perform bifurcation analysis directly during experimental tests. Although CBC has been successfully demonstrated on…
The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will…
Computing the receding horizon optimal control of nonlinear hybrid systems is typically prohibitively slow, limiting real-time implementation. To address this challenge, we propose a layered Model Predictive Control (MPC) architecture for…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
The problem of partial stabilization for nonlinear control systems described by the Ito stochastic differential equations is considered. For these systems, we propose a constructive control design method which leads to establishing the…
The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…