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We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
In this paper, conformal fractional order discretization [20, 24, 25] is used to analyze bifurcation analysis and stability of a predator-prey system. A continuous model has been discretized into a discrete one while preserving the…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
In the present work, we propose a new parameterization for the concentration flux using fractional derivatives. The fractional order differential equation in the longitudinal and vertical directions is used to obtain the concentration…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
Distributed algorithms for both discrete-time and continuous-time linearly solvable optimal control (LSOC) problems of networked multi-agent systems (MASs) are investigated in this paper. A distributed framework is proposed to partition the…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
This paper introduces a test for fractional integration in a model that possibly contains smooth deterministic trends. We model the trend component using a Chebyshev polynomial and specify the short-run dynamics semi-parametrically,…
Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under…
Phase separation accompanied by further domain growth and coarsening is a phenomenon common to a broad variety of dynamical systems. In this connection, controlling such processes represents a relevant interdisciplinary problem. Using…
It has been recognized that using time-varying initialization functions to solve the initial value problem of fractional-order systems (FOS) is both complex and essential in defining the dynamical behavior of the states of FOSs. In this…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
In this paper, we introduce the new construction of fractional derivatives and integrals with respect to a function, based on a matrix approach. We believe that this is a powerful tool in both analytical and numerical calculations. We begin…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
In this paper, fractional order Coullet system is studied. An active control technique is applied to control this chaotic system. This type of controller is also applied to synchronize chaotic fractional-order systems in master-slave…
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a…
In this paper we will present a mathematical description and analysis of a fractional-order regulated system in the state space and the state-space controller design based on placing the closed-loop poles on the complex plane. Presented are…