Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Stabilization of stochastic dynamical systems of a random structure with Markov switches and Poisson perturbations

An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps, which makes the system stable in probability. Sufficient conditions of the stability in probability are obtained, using the second Lyapunov method, in which the construction of the corresponding functions plays an important role. Here we provide a solution to the problem of optimal stabilization in a general case. For a linear system with a quadratic quality function, we give a method of synthesis of optimal control based on the solution of Riccati equations. Finally, in an autonomous case, a system of differential equations was constructed to obtain unknown matrices that are used for the building of an optimal control. The method of a small parameter is justified for the algorithmic search of an optimal control. This approach brings a novel solution to the problem of optimal stabilization for a stochastic dynamical system with a random structure, Markov switches and Poisson perturbations.Comment: 15 pages, 0 figures, 25 reference

Measurement Of The Responses Of Polyurethane And Confortm Foams And The Development Of A System Identification Technique To Estimate Polyurethane Foam Parameters From Experimental Impulse Responses

Flexible polyurethane foam is the main cushioning element used in car seats. Optimization of an occupied seat\u27s static and dynamic behavior requires models of foam that are accurate over a wide range of excitation and pre-compression conditions. Experiments were conducted to measure the response of foam over a wide range of excitation which include slowly varying uniaxial compression tests on a 3 inch cube foam sample, base excitation and impulse excitation test on a foam-mass system. The foam used was the same in all of the experiments, thus obtaining all the responses on the same foam sample which helps eliminate the sample to sample variation. Similar efforts were taken to conduct impulse and base excitation tests on CONFOR(TM) foam to help in future modeling efforts of CONFOR(TM) foam. All the experimental protocols and data pre-processing protocols along with results are presented. Previous researcher developed a linear model for a single-degree of freedom foam-mass system subjected to an impulsive excitation. Free response data from impulse tests on a foam-mass system with different masses was used to identify model parameters at various pre-compression levels (settling points). The free response of the system was modeled as a Prony series (sum of exponentials) whose parameters can be related to the parameters in the foam-mass system model. Models identified from tests at one settling point performed poorly when used to predict the response at other settling points. In this research, a method is described to estimate the parameters of a global model of the foam behavior from data gathered in a series of impulse tests at different settling points. The global model structure includes a nonlinear elastic term and a hereditary viscoelastic term. The model can be used to predict the settling point for each mass used and, by expanding the model about that settling point, local linear models of the response to impulsive excitation can be derived. From this analysis the relationship between the local linear model parameters and the global model parameters was defined. A series of experiments were conducted using different sized masses on the foam block. For each mass, the settling point was measured and the free response after an impulsive excitation was modeled as a Prony series whose parameters can be related to the parameters in the local linear dynamic model. By using the relationship between the local and global model parameters and estimates of the local models\u27 parameters, the parameters of the global model were estimated. The estimation method was first applied to simulation data and then used to identify models of the uniaxial dynamic behavior of polyurethane foam blocks

Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks

Closed-loop iterative learning control for fractional-order linear singular time-delay system: PDα-type

U ovom radu razmatrano je iterativno upravljanje učenjem u zatvorenoj petlji (ILC) - PDα tip linearnim singularnim sistemom sa kašnjenjem necelog reda. Dati su dovoljni uslovi za konvergenciju u vremenskom domenu predloženog PD-alfa tipa ILC za datu klasu linearnog singularnog sistema sa kašnjenjem necelog reda zajedno sa odgovarajućom teoremom i dokazom. Takođe, po prvi put je u ovom radu predloženi tip PDα ILC primenjen za datu klasu linearnih singularnih sistema sa kašnjenjem necelog reda sa neizvesnošću. Konačno, valjanost predloženog ILC algoritma upravljanja za razmatranu klasu singularnih sistema je potvrđena sa adekvatnom numeričkom simulacijom.In this paper a closed-loop PDα - type iterative learning control (ILC) of fractional order linear singular time-delay system is considered. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Also, for the first time, we proposed a proposed ILC PDα type for a given class of uncertain, fractional order, singular systems. Finally, the validity of the proposed PDα ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515

A theoretical investigation of the effect of proliferation and\ud adhesion on monoclonal conversion in the colonic crypt

Colorectal cancers are initiated by the accumulation of mutations in the colonic epithelium. Using a spatially structured cell-based model of a colonic crypt, we investigate the likelihood that the progeny of a mutated cell will dominate, or be sloughed out of, a crypt. Our approach is to perform multiple simulations, varying the spatial location of the initial mutation, and its proliferative and adhesive properties, to obtain statistical distributions for the probability of domination. Our simulations lead us to make a number of predictions. The process of monoclonal conversion always occurs, and does not require that the cell which initially gave rise to the population remains in the crypt. Mutations occurring more than one to two cells from the base of the crypt are unlikely to become the dominant clone. The probability of a mutant clone persisting in the crypt is sensitive to dysregulation of adhesion, and comparison with a one-dimensional model suggests that this is caused by competition directly at the base of the crypt.\ud We also predict that increases in the extent of the spatial domain in which the mutant cells proliferate cause counter-intuitive non-linear changes to the probability of its fixation, due to effects that cannot be captured in simpler models

Stability, observer design and control of networks using Lyapunov methods

We investigate different aspects of the analysis and control of interconnected systems. Different tools, based on Lyapunov methods, are provided to analyze such systems in view of stability, to design observers and to control systems subject to stabilization. All the different tools presented in this work can be used for many applications and extend the analysis toolbox of networks. Considering systems with inputs, the stability property input-to-state dynamical stability (ISDS) has some advantages over input-to-state stability (ISS). We introduce the ISDS property for interconnected systems and provide an ISDS small-gain theorem with a construction of an ISDS-Lyapunov function and the rate and the gains of the ISDS estimation for the whole system. This result is applied to observer design for single and interconnected systems. Observers are used in many applications where the measurement of the state is not possible or disturbed due to physical reasons or the measurement is uneconomical. By the help of error Lyapunov functions we design observers, which have a so-called quasi ISS or quasi-ISDS property to guarantee that the dynamics of the estimation error of the systems state has the ISS or ISDS property, respectively. This is applied to quantized feedback stabilization. In many applications, there occur time-delays and/or instantaneous jumps of the systems state. At first, we provide tools to check whether a network of time-delay systems has the ISS property using ISS-Lyapunov-Razumikhin functions and ISS-Lyapunov-Krasovskii functionals. Then, these approaches are also used for interconnected impulsive systems with time-delays using exponential Lyapunov-Razumikhin functions and exponential Lyapunov-Krasovskii functionals. We derive conditions to assure ISS of an impulsive network with time-delays. Controlling a system in a desired and optimal way under given constraints is a challenging task. One approach to handle such problems is model predictive control (MPC). In this thesis, we introduce the ISDS property for MPC of single and interconnected systems. We provide conditions to assure the ISDS property of systems using MPC, where the previous result of this thesis, the ISDS small-gain theorem, is applied. Furthermore, we investigate the ISS property for MPC of time-delay systems using the Lyapunov-Krasovskii approach. We prove theorems, which guarantee ISS for single and interconnected systems using MPC