Sanja Zivanovic

Sanja Zivanovic
Barry University · Mathematics and Computer Science

PhD

About

16
Publications
1,231
Reads
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96
Citations
Citations since 2016
6 Research Items
50 Citations
20162017201820192020202120220246810
20162017201820192020202120220246810
20162017201820192020202120220246810
20162017201820192020202120220246810
Additional affiliations
August 2011 - February 2021
Barry University
Position
  • Chair
August 2011 - present
Barry University
Position
  • Professor (Assistant)
June 2009 - November 2010
Centrum Wiskunde & Informatica
Position
  • PostDoc Position
Description
  • Worked on developing an algorithm for computation of reachable sets of differential inclusions.

Publications

Publications (16)
Article
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...
Preprint
Full-text available
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...
Chapter
Full-text available
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...
Article
Full-text available
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...
Conference Paper
Full-text available
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....
Conference Paper
Full-text available
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...
Chapter
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
Full-text available
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...
Conference Paper
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...

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Projects

Projects (2)
Project
A C++ library for formal verification of nonlinear hybrid systems through reachability analysis.