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This paper presents a novel approach in designing neural network based adaptive controllers for a class of nonlinear discrete-time systems. This type of controllers has its simplicity in parallelism to linear generalized minimum variance (GMV) controller design and efficiency to deal with complex nonlinear dynamics. A recurrent neural network is introduced as a bridge to compensation simplify controller design procedure and efficiently to deal with nonlinearity. The network weight adaptation law is derived from Lyapunov stability analysis and the connection between convergence of the network weight and the reconstruction error of the network is established. A theorem is presented for the conditions of the stability of the closed-loop systems. Two simulation examples are provided to demonstrate the efficiency of the approach.
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http://dx.doi.org/10.1109/TNN.2004.826131 | DOI Listing |
Neural Netw
December 2024
Air and Missile Defense College, Air Force Engineering University, Xi'an, 710051, Shanxi, China. Electronic address:
Most existing results on prescribed performance control (PPC), subject to input saturation and initial condition limitations, focus on continuous-time nonlinear systems. This article, as regards discrete-time nonlinear systems, is dedicated to constructing a novel adaptive switching control strategy to circumvent the singular problem when the PPC undergoes input saturation, while the initial conditions of the system can be released under the framework of PPC. The main design steps and characteristics include: (1) By devising a new discrete-time global finite-time performance function (DTGFTPF), the constructed performance boundary is shown to survive insensitive to arbitrary initial values, which present in the system; (2) A discrete-time adaptive finite-time prescribed performance controller (DTAFPPC) and a discrete-time adaptive backstepping controller (DTABC) are constructed, simultaneously.
View Article and Find Full Text PDFChaos
December 2024
Differential Equations, Modeling and Simulation Group, Department of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, Madhya Pradesh, India.
This paper presents a comprehensive analysis of a discrete-time predator-prey model within a homogeneous two-patch environment, incorporating both prey and predator dispersal. We consider a logistic growth for both prey and predator species, and the predation process is based on the Holling type-II functional response in the isolated patches. We explore the existence of multiple coexisting equilibria and establish their stability conditions.
View Article and Find Full Text PDFChaos
December 2024
Department of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, Madhya Pradesh, India.
This paper explores a discrete-time system derived from the well-known continuous-time Rosenzweig-MacArthur model using the piecewise constant argument. Examining the impact of increasing carrying capacity and harvesting efforts, we uncover intricate phenomena, such as periodicity, quasiperiodicity, period-doubling, period-bubbling, and chaos. Our analysis reveals that increasing the carrying capacity of prey species can lead to both system stabilization and destabilization.
View Article and Find Full Text PDFJ Magn Reson
December 2024
Department of Physics, University of Maryland Baltimore County, Baltimore, MD 21250, USA. Electronic address:
In this paper, we numerically optimize broadband pulse shapes that maximize Hahn echo amplitudes. Pulses are parameterized as neural networks (NN), nonlinear amplitude limited Fourier series (FS), and discrete time series (DT). These are compared to an optimized choice of the conventional hyperbolic secant (HS) pulse shape.
View Article and Find Full Text PDFStat Methods Med Res
October 2024
Department of Economics, Massachusetts Institute of Technology, Cambridge, MA, USA.
We describe a novel approach for recovering the underlying parameters of the SIR dynamic epidemic model from observed data on case incidence. We formulate a discrete-time approximation of the original continuous-time model and search for the parameter vector that minimizes the standard least squares criterion function. We show that the gradient vector and matrix of second-order derivatives of the criterion function with respect to the parameters adhere to their own systems of difference equations and thus can be exactly calculated iteratively.
View Article and Find Full Text PDFEnter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!