Neural-network approximation of piecewise continuous functions: application to friction compensation

2002 ◽  
Vol 13 (3) ◽  
pp. 745-751 ◽  
Author(s):  
R.R. Selmic ◽  
F.L. Lewis
Keyword(s):  
Neural Network ◽  
Continuous Functions ◽  
Friction Compensation ◽  
Piecewise Continuous

Artificial Polynomial and Trigonometric Higher Order Neural Network Group Models

2013 ◽  
pp. 78-102 ◽  
Author(s):  
Ming Zhang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Continuous Function ◽  
Trigonometric Polynomial ◽  
Network Models ◽  
Higher Order ◽  
Financial Data ◽  
Neural Network Models ◽  
Piecewise Continuous ◽  
Discontinuous Data

Real world financial data is often discontinuous and non-smooth. Accuracy will be a problem, if we attempt to use neural networks to simulate such functions. Neural network group models can perform this function with more accuracy. Both Polynomial Higher Order Neural Network Group (PHONNG) and Trigonometric polynomial Higher Order Neural Network Group (THONNG) models are studied in this chapter. These PHONNG and THONNG models are open box, convergent models capable of approximating any kind of piecewise continuous function to any degree of accuracy. Moreover, they are capable of handling higher frequency, higher order nonlinear, and discontinuous data. Results obtained using Polynomial Higher Order Neural Network Group and Trigonometric polynomial Higher Order Neural Network Group financial simulators are presented, which confirm that PHONNG and THONNG group models converge without difficulty, and are considerably more accurate (0.7542% - 1.0715%) than neural network models such as using Polynomial Higher Order Neural Network (PHONN) and Trigonometric polynomial Higher Order Neural Network (THONN) models.

scholarly journals Disturbance Observer-Based Adaptive Neural Network Control of Marine Vessel Systems with Time-Varying Output Constraints

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wei Zhao ◽  
Li Tang ◽  
Yan-Jun Liu
Keyword(s):  
Neural Network ◽  
Disturbance Observer ◽  
Continuous Functions ◽  
Network Control ◽  
Time Varying ◽  
Adaptive Neural Network ◽  
External Disturbances ◽  
Adaptive Neural Network Control ◽  
Output Constraints ◽  
Novel Strategy

This article investigates an adaptive neural network (NN) control algorithm for marine surface vessels with time-varying output constraints and unknown external disturbances. The nonlinear state-dependent transformation (NSDT) is introduced to eliminate the feasibility conditions of virtual controller. Moreover, the barrier Lyapunov function (BLF) is used to achieve time-varying output constraints. As an important approximation tool, the NN is employed to approximate uncertain and continuous functions. Subsequently, the disturbance observer is structured to observe time-varying constraints and unknown external disturbances. The novel strategy can guarantee that all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, the simulation results verify the benefit of the proposed method.

Note on an Application of the δ-Function in the Representation of Solutions of Algebraic Equations

1967 ◽  
Vol 10 (5) ◽  
pp. 735-738
Author(s):  
J. B. Sabat
Keyword(s):  
Continuous Function ◽  
Delta Function ◽  
Continuous Functions ◽  
Dirac Delta Function ◽  
Algebraic Equations ◽  
Dirac Delta ◽  
Representation Of Solutions ◽  
Piecewise Continuous ◽  
Image Position

The “function” δ(x - xo) is known as the Dirac Delta function and may be defined as zero everywhere except at xo, where it is infinite in such a way that1having property that for every continuous function φ(x) on (a, b)2It is well known [2] δ(x-xo) can be approximated as a limit of a sequence of piecewise continuous functions, and there is an abundance of such sequences.

Some explicit results on one kind of sticky diffusion

2019 ◽  
Vol 56 (2) ◽  
pp. 398-415
Author(s):  
Yiming Jiang ◽  
Shiyu Song ◽  
Yongjin Wang
Keyword(s):  
Diffusion Process ◽  
Continuous Functions ◽  
Price Dynamics ◽  
Call Option ◽  
Distributional Properties ◽  
Financial Application ◽  
Piecewise Continuous

AbstractIn this paper we derive several explicit results on one special sticky diffusion process which is constructed as a time-changed version of a diffusion with no sticky points. A theorem concerning the process-related Green operators defined on some nonnegative piecewise continuous functions is provided. Then, based on this theorem, we explore the distributional properties of the sticky diffusion. A financial application is presented where we compute the value of the European vanilla call option written on the underlying with sticky price dynamics.

scholarly journals Neural networks-based robust adaptive flight path tracking control of large transport

2018 ◽  
Vol 38 (3) ◽  
pp. 268-278
Author(s):  
Maolong Lv ◽  
Xiuxia Sun ◽  
G. Z. Xu ◽  
Z. T. Wang
Keyword(s):  
Neural Network ◽  
Control Method ◽  
Nonlinear Modeling ◽  
Dynamic Surface Control ◽  
Continuous Functions ◽  
Network Dynamic ◽  
Dynamic Surface ◽  
The Neural Network ◽  
Neural Network Dynamic ◽  
Robust Adaptive

For the ultralow altitude airdrop decline stage, many factors such as actuator nonlinearity, the uncertain atmospheric disturbances, and model unknown nonlinearity affect the precision of trajectory tracking. A robust adaptive neural network dynamic surface control method is proposed. The neural network is used to approximate unknown nonlinear continuous functions of the model, and a nonlinear robust term is introduced to eliminate the actuator’s nonlinear modeling error and external disturbances. From Lyapunov stability theorem, it is rigorously proved that all the signals in the closed-loop system are bounded. Simulation results confirm the perfect tracking performance and strong robustness of the proposed method.

scholarly journals Synthesis of intelligent fuzzy control in the space of bounded piecewise-continuous functions based on the combined maximum principle

2018 ◽  
Vol 226 ◽  
pp. 04031 ◽  
Author(s):  
Andrey A. Kostoglotov ◽  
Sergey V. Lazarnko ◽  
Igor A. Nikitin
Keyword(s):  
Control Method ◽  
Control Object ◽  
Continuous Functions ◽  
Terminal State ◽  
Control Synthesis ◽  
Continuous Control ◽  
Control Laws ◽  
Relay Control ◽  
Piecewise Continuous ◽  
Two Stages

It is shown that the solution of the problem of control synthesis using the Hamilton-Ostrogradskii principle leads to a variational inequality, from which the conditions for the maximum of the the generalized power function in the space of bounded piecewise continuous functions follow. It allows to find a feedback structure up to a synthesis function. Using the methods of the structure construction the nonlinear structures of the relay and continuous control laws are obtained. The proposed control method allows to avoid the mode with frequented switching. It consists of the following two stages. At the first stage, the control object is brought into the vicinity of the terminal state using the relay control law. In the second stage, the quasi-optimal continuous control is used. The uncertainty of the transition area size is resolved using fuzzy logic. The efficiency of the intelligent controls is demonstrated by the example of mathematical modeling of the system dynamics.

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