20,022 research outputs found
Learning Optimal Control of Synchronization in Networks of Coupled Oscillators using Genetic Programming-based Symbolic Regression
Networks of coupled dynamical systems provide a powerful way to model systems
with enormously complex dynamics, such as the human brain. Control of
synchronization in such networked systems has far reaching applications in many
domains, including engineering and medicine. In this paper, we formulate the
synchronization control in dynamical systems as an optimization problem and
present a multi-objective genetic programming-based approach to infer optimal
control functions that drive the system from a synchronized to a
non-synchronized state and vice-versa. The genetic programming-based controller
allows learning optimal control functions in an interpretable symbolic form.
The effectiveness of the proposed approach is demonstrated in controlling
synchronization in coupled oscillator systems linked in networks of increasing
order complexity, ranging from a simple coupled oscillator system to a
hierarchical network of coupled oscillators. The results show that the proposed
method can learn highly-effective and interpretable control functions for such
systems.Comment: Submitted to nonlinear dynamic
Fractional Order Version of the HJB Equation
We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB)
equation for fractional order dynamical systems in which a generalized
performance index is considered for the related optimal control problem. Owing
to the nonlocality of the fractional order operators, the classical HJB
equation, in the usual form, does not hold true for fractional problems.
Effectiveness of the proposed technique is illustrated through a numerical
example.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN
1555-1423, CODEN: JCNDDM. Submitted 28-June-2018; Revised 15-Sept-2018;
Accepted 28-Oct-201
Mathematical problems for complex networks
Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy
is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics
PVT-Robust CMOS Programmable Chaotic Oscillator: Synchronization of Two 7-Scroll Attractors
Designing chaotic oscillators using complementary metal-oxide-semiconductor (CMOS) integrated circuit technology for generating multi-scroll attractors has been a challenge. That way, we introduce a current-mode piecewise-linear (PWL) function based on CMOS cells that allow programmable generation of 2–7-scroll chaotic attractors. The mathematical model of the chaotic oscillator designed herein has four coefficients and a PWL function, which can be varied to provide a high value of the maximum Lyapunov exponent. The coefficients are implemented electronically by designing operational transconductance amplifiers that allow programmability of their transconductances. Design simulations of the chaotic oscillator are provided for the 0.35μ m CMOS technology. Post-layout and process–voltage–temperature (PVT) variation simulations demonstrate robustness of the multi-scroll chaotic attractors. Finally, we highlight the synchronization of two seven-scroll attractors in a master–slave topology by generalized Hamiltonian forms and observer approach. Simulation results show that the synchronized CMOS chaotic oscillators are robust to PVT variations and are suitable for chaotic secure communication applications.Universidad Autónoma de Tlaxcala CACyPI-UATx-2017Program to Strengthen Quality in Educational Institutions C/PFCE-2016-29MSU0013Y-07-23National Council for Science and Technology 237991 22284
E&F Chaos: a user friendly software package for nonlinear economic dynamics
The use of nonlinear dynamic models in economics and finance has expanded rapidly in the last two decades. Numerical simulation is crucial in the investigation of nonlinear systems. E&F Chaos is an easy-to-use and freely available software package for simulation of nonlinear dynamic models to investigate stability of steady states and the presence of periodic orbits and chaos by standard numerical simulation techniques such as time series, phase plots, bifurcation diagrams, Lyapunov exponent plots, basin boundary plots and graphical analysis. The package contains many well-known nonlinear models, including applications in economics and finance, and is easy to use for non-specialists. New models and extensions or variations are easy to implement within the software package without the use of a compiler or other software. The software is demonstrated by investigating the dynamical behavior of some simple examples of the familiar cobweb model, including an extension with heterogeneous agents and asynchronous updating of strategies. Simulations with the E&F chaos software quickly provide information about local and global dynamics and easily lead to challenging questions for further mathematical analysis.
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
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