# Sanja ZivanovicBarry University · Mathematics and Computer Science

Sanja Zivanovic

PhD

## About

16

Publications

1,231

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96

Citations

Citations since 2016

Introduction

## Publications

Publications (16)

Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal...

Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal...

Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal...

Unmanned aerial vehicles (UAVs), also known as drones have many applications and they are a current trend across many industries. They can be used for delivery, sports, surveillance, professional photography, cinematography, military combat, natural disaster assistance, security, and the list grows every day. Programming opens an avenue to automate...

Cyber-physical systems (CPS) are hybrid systems that commonly consist of a discrete control part that operates in a continuous environment. Hybrid automata are a convenient model for CPS suitable for formal verification. The latter is based on reachability analysis of the system to trace its hybrid evolution and consequently verify its properties....

We are interested in time evolution of systems that switch their modes of operation at discrete moments of time. The intervals between switching may, in general, vary. The number of modes may be finite or infinite. The mathematical setting for such systems is variable time step dynamics with choice. We have used this setting previously to study the...

Differential inclusions are mathematical models of nondeterministic continuous-time systems for which no stochastic information on the behavior is known. They arise naturally as reduced models of deterministic systems or as models of components of a distributed system with partial knowledge of the inputs. In order to verify that such systems satisf...

We develop a simple and general approach to study long term behavior of deterministic sys-tems that switch regimes and have dwell times of variable length. We investigate the results of all possible as well as restricted, and/or controlled, switchings. To analyze all these situations, we introduce the notions of variable time step dy-namics with ch...

Given a map Φ defined on bounded subsets of the (base) metric space X and with bounded sets as its values, one can follow the orbits A, Φ (A), Φ2(A), …, of nonempty, closed, and bounded sets A in X. This is the system (Φ, X). On the other hand, the same orbits can be viewed as trajectories of points in the hyperspace X♯ of nonempty, closed, and bou...

We present a numerical method for rigorous over-approximation of a reachable
set of differential inclusions. The method gives high-order error bounds for
single step approximations and a uniform bound on the error over the finite
time interval. We provide formulas for the local error based on Lipschitz
constants and bounds on higher-order derivativ...

Mathematical setting for discrete dynamics is a state space, X, and a map S: X → X (the evolution operator) which defines the change of a state over one time step. Dynamics with choice, as we define it in [2], is a generalization of discrete dynamics where at every time step there is not one but several available maps that can transform the current...

A numerical method for rigorous over-approximation of a solution set of an input-affine system whose inputs represent some bounded noise is presented. The method gives high order error for a single time step and a uniform bound on the error over the finite time interval. The approach is based on the approximations of inputs by linear functions at e...

Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. This notion is new and interesting from the mathematical point of view. At the same time, many real life processes studied in chemical physics...

We studied the influence of inorganic salts and bases on the absorption spectra and kinetics of the formation of the J-band in water solutions of 1,1‘-diethyl-2, 2‘-cyanine (PIC) iodide. The absorption spectra of diluted (10-5 to 10-6 mol/L) solutions of PIC containing significant amounts of neutral or basic inorganic salts showed an intense and na...

Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. Many real life processes studied in chemical physics, engineering, biology and medicine, from autocatalytic reaction systems to switched syste...

## Projects

Projects (2)

A C++ library for formal verification of nonlinear hybrid systems through reachability analysis.