Nonlinear Dynamics of Interconnected Systems Research Group 

Systems of communicating components are crucial in a broad range of applications including space exploration, mobile sensor networks, teleoperated surgical robots, control of teams of vehicles, and integrated building systems. Interconnections are not only manifested by a communication channel, but by the inherent coupling of the states in the equations describing the system. The analysis of communicating dynamic components is timely and important.

We envision controlling fleets of drones to act as sensor networks for computing acoustic/heat maps and measuring pollutant dispersion. The studies will impact emergency response operations, saving human lives and minimizing environmental/urban damage.
The fundamental contribution of our research is a novel theoretical and computational framework for studying stability and performance of interconnected systems.
The research goal of our integrated research and educational endeavor is to advance the understanding of the behavior of interconnected systems through a hybrid system formulation, leading to the evaluation of random matrix products. The novelty of our research lies in expressing the Lyapunov exponent –a measure of stability- as a path average and characterizing the discrete structure associated with the hybrid system (the underlying graph). The statistical properties of the induced random walk on the underlying graphs will be used to quantify stability and performance properties of the system. This is achieved by combining techniques and tools of dynamical systems techniques, discrete mathematics and statistical physics.

Team Members

Tamás Kalmár-Nagy, PhD
Lead researcher

Research interest
  • Control theory
  • Numerical analysis
  • Nonlinear analysis
  • Modal analysis
  • Turbulence modelling
  • Robotics
Contacts

Bendegúz Dezső Bak, PhD

Research interest
  • Percolation models - flow in porous media
  • Energy transfer in chain oscillators
  • Travelling Salesman Problem, Multi Agent Planning Problem
  • Computational Fluid Dynamics
Contacts

János Lelkes, MSc

Research interest
  • Delay differential equations
  • Bifurcation analysis
  • Perturbation techniques
  • Aeroelasticity
Contacts

Csanád Árpád Hubay, MSc

Research interest
  • Analytic differential equations - normal forms, degenerate equilibriums
  • Nonlinear oscillators
  • Carleman linearization and its applications
  • Parametrically excited systems
Contacts

Ádám Zsiros, MSc

Research interest
  • Mechanistic turbulence model
  • Rod models
  • Energy transfer
  • Energy spectrum
Contacts

Research Projects

GAME OF DRONES

We are building a drone fleet with the purpose of wind-tunnel and outdoor testing of communication protocols, control algorithms and distributed sensor networks.

TRAJECTORY GENERATION FOR ROBOTIC SYSTEMS

In applications it is often necessary to solve the path planning problem many times a second, thus real-time trajectory generation for various vehicles remain an important topic for robotics research. Apply a control method (e.g. constrained dynamic inversion) for trajectory generation.

Projects for Students

LIQUID DRAINAGE THROUGH REGULAR NETWORK

We simulate the propagation of non-wetting fluid through porous medium. A resistance is assigned to each element of the network which must be defeated by the external liquid pressure. We investigate the saturation of the network as function of the appéied pressure. So far we only dealt with regular square networks, but we want to carry out simulations on other types of networks. Apply now!

MECHANISTIC MODEL OF TURBULENCE

Understanding turbulent flows is one of the biggest challenges in the field of fluid mechanics. The subject of my research is a mass-spring-damper system arranged in a binary tree. The goal is to study the energy transfer among the different scales of elements. The hierarchical arrangement represents the connection among the eddies of different sizes. The task is to build-in different mechanical elements and analyze the system. Apply now!

SUPPRESSING FLUTTER VIBRATIONS BY PARAMETRIC INERTIA EXCITATION

We will study a slender elastic engineering structure with lateral and angular deflections under the action of flow-induced vibrations. This aeroelastic instability excites and couples the system’s bending and torsion modes. We will apply parametric excitation to stabilize this self-excitation mechanism. The parametric excitation mechanism is modeled by time-harmonic variation in the concentrated mass and/or moment of inertia. Apply now!

APPLICATION OF MODELING TOOL FOR AEROELASTIC STUDIES

We will learn about modeling and simulation of aeroelastic rectangular wings. A state-space aeroelastic model will be used for analysis. The flutter speed and frequency for a clamped plate will be computed using damping-versus-velocity and frequency-versus-velocity analysis. Apply now!


Click here for all the available projects at the Department of Fluid Mechanics, BME.

Contact Us

Please, contact us if you have any questions about our research projects!