Related papers: Theoretical Design and FPGA-Based Implementation o…
In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
Chaotic systems have been investigated in several areas of engineering. In control theory, such systems have instigated the emergence of new techniques as well, have been used as a source of noise generation. The application of chaotic…
Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a broad audience and has been the subject of thousands of…
A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable…
In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to…
We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible…
Fault tolerance is increasingly being use to design Dependable Digital Systems (DDS), which refers to the capability of a system to keep performing its intended functions in existence of faults. DDS are typically used in Safety-critical…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
In this paper, we present an approach for designing correct-by-design controllers for cyber-physical systems composed of multiple dynamically interconnected uncertain systems. We consider networked discrete-time uncertain nonlinear systems…