Other Research Areas

Application of Dynamical Systems

Dynamical systems describe the time-evolution of a state vector. The state vector characterizes (usually completely) the posture, status or mode of a given system. Dynamical systems in contrast to algebraic systems account for the time-evolution and transient conditions within a system. Thus the dynamics of a given system are considered to have died out when at state-state.

Dynamical systems are typically described by ordinary differential equations (continuous-time) or ordinary difference equations (discrete-time). Visually, the behavior of a dynamical system is shown as motion of a state vector in an appropriate state-space. Nonlinear dynamical systems allow for rich behavior that can be employed for lightweight modeling of a variety of systems. Our research focuses on harnessing such systems for modeling (e.g., smart grid systems) and robotic systems.

Related Publications

K. Aljanaideh; M. Al Janaideh; M. Rakotondrabe; D. Kundur

Identification of Piezomicropositioning Hammerstein Systems with Generalized Prandtl-Ishlinskii Hysteresis Nonlinearities Inproceedings

Proc. IEEE Conference on Decision and Control, Miami Beach, Florida, 2018.

BibTeX

K. Aljanaideh; M. Rakotondrabe; M. Al Janaideh; D. Kundur

Identification of Precision Motion Systems with Prandtl-Ishlinskii Hysteresis Nonlinearities Inproceedings

Proc. American Control Conference, pp. to appear, 2018.

BibTeX

D. Kundur; X. Feng; S. Mashayekh; S. Liu; T. Zourntos; K.L. Butler-Purry

Towards Modeling the Impact of Cyber Attacks on a Smart Grid Journal Article

International Journal of Security and Networks, 6 (1), pp. 2-13, 2011.

BibTeX | Links:

N. J. Mathai; T. Zourntos; D. Kundur

Vector Field Driven Design for Lightweight Signal Processing and Control Schemes for Autonomous Robotic Navigation Journal Article

EURASIP Journal on Advances in Signal Processing Special Issue on Signal Processing Advances in Robots and Autonomy, 2009 (Article ID 984752), pp. 9, 2009.

BibTeX | Links:

Nebu John Mathai

Cybernetic Automata: An Approach for the Realization of Economical Cognition for Multi-Robot Systems PhD Thesis

Texas A&M University, 2008, ((Winner of TAMU 2008 U.S. Senator Phil Gramm Doctoral Award)).

Abstract | BibTeX

@phdthesis{MatPhDThesis08,
title = {Cybernetic Automata: An Approach for the Realization of Economical Cognition for Multi-Robot Systems},
author = {Nebu John Mathai},
year = {2008},
date = {2008-05-01},
address = {College Station, TX},
school = {Texas A&M University},
abstract = {(Winner of TAMU 2008 U.S. Senator Phil Gramm Doctoral Award)

The multi-agent robotics paradigm has attracted much attention due to the variety of pertinent applications that are well-served by the use of a multiplicity of agents (including space robotics, search and rescue, and mobile sensor networks). The use of this paradigm for most applications, however, demands economical, lightweight agent designs for reasons of longer operational life, lower economic cost, faster and easily-verified designs, etc.

An important contributing factor to an agent’s cost is its control architecture. Due to the emergence of novel implementation technologies carrying the promise of economical implementation, we consider the development of a technology-independent specification for computational machinery. To that end, the use of cybernetics toolsets (control and dynamical systems theory) is appropriate, enabling a principled specification of robotic control architectures in mathematical terms that could be mapped directly to diverse implementation substrates.

This dissertation, hence, addresses the problem of developing a technologyindependent specification for lightweight control architectures to enable robotic agents to serve in a multi-agent scheme. We present the principled design of static and dynamical regulators that elicit useful behaviors, and integrate these within an overall architecture for both single and multi-agent control. Since the use of control theory can be limited in unstructured environments, a major focus of the work is on the engineering of emergent behavior.

The proposed scheme is highly decentralized, requiring only local sensing and no inter-agent communication. Beyond several simulation-based studies, we provide experimental results for a two-agent system, based on a custom implementation employing field-programmable gate arrays.},
type = {Ph.D. Thesis},
note = {(Winner of TAMU 2008 U.S. Senator Phil Gramm Doctoral Award)},
keywords = {},
pubstate = {published},
tppubtype = {phdthesis}
}

T. Zourntos; N. J. Mathai; S. Magierowski; D. Kundur

A Bio-inspired Analog Scheme for Navigational Control of Lightweight Autonomous Agents Inproceedings

Proc. IEEE International Conference on Robotics and Automation (ICRA), pp. 1132-1137, Pasadena, California, 2008.

BibTeX | Links:

N. J. Mathai; T. Zourntos; D. Kundur

Vector Field Design of Screw-Type Chaos Journal Article

Fluctuations and Noise Letters, 8 (3-4), pp. L369-L379, 2008.

BibTeX | Links: