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Control Occupation Kernel Regression for Nonlinear Control-Affine Systems [article]

Moad Abudia, Tejasvi Channagiri, Joel A. Rosenfeld, Rushikesh Kamalapurkar
2021 arXiv   pre-print
This manuscript presents an algorithm for obtaining an approximation of nonlinear high order control affine dynamical systems, that leverages the controlled trajectories as the central unit of information  ...  Interestingly, the vector valued structure of the Hilbert space allows for simultaneous approximation of the drift and control effectiveness components of the control affine system.  ...  Acknowledgments and Disclosure of Funding  ... 
arXiv:2106.00103v1 fatcat:nw7dqfi4vnetbo664v6keqfdkq

Adaptive Fuzzy Sliding Mode Control for a Model-Scaled Unmanned Helicopter

Amir Razzaghian, Reihaneh Kardehi Moghaddam
2016 Journal of Fuzzy Set Valued Analysis  
First, in order to efficient control law design, the nonlinear model of the helicopter is reformulated as an affine nonlinear system.  ...  To verify the merits of the proposed controller, it is compared with traditional sliding mode control system.  ...  Affine Nonlinear Systems Control Using Traditional Sliding Mode Control Consider a typical ℎ order affine nonlinear system as: If is chosen as ≥ then, the closed loop control system using this control  ... 
doi:10.5899/2016/jfsva-00356 fatcat:c5rihrjgj5bojkml4egx2n5pzm

Complexity Analysis of the Piece-Wise Affine Approximation for the Car on the Nonlinear Hill Model Related To Discrete–Time, Minimum Time Control Problem

P. Orlowski
2014 Elektronika ir Elektrotechnika  
Accuracy and numerical complexity of the piece-wise affine control system grow with the number of polyhedral partitions, that describe the system.  ...  The main aim of the paper is to analyse effectiveness of the approximation method from the nonlinear discretised into discrete piece-wise affine model.  ...  The main aim of the paper is to propose and evaluate method for piecewise affine approximation of nonlinear system.  ... 
doi:10.5755/j01.eee.20.10.4454 fatcat:sfk6lk2pyjfntei2qvr4y3ugri

On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models

T.A. Johansen, R. Shorten, R. Murray-Smith
2000 IEEE transactions on fuzzy systems  
of the nonlinear dynamic system.  ...  This defines a multi-objective identification problem, namely, the construction of a dynamic model that is a good approximation of both local and global dynamics of the underlying system.  ...  Obviously, the higher order terms in (10) and (8) are of different order. B. Approximation Theorem Assume a continuous trajectory that satisfies is given, and .  ... 
doi:10.1109/91.855918 fatcat:jqnma2ocu5darkvhevhvtpn3re

Generalized Hamilton–Jacobi–Bellman Formulation -Based Neural Network Control of Affine Nonlinear Discrete-Time Systems

Zheng Chen, S. Jagannathan
2008 IEEE Transactions on Neural Networks  
The definition of GHJB, pre-Hamiltonian function, HJB equation, and method of updating the control function for the affine nonlinear DT systems under small perturbation assumption are proposed.  ...  In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time (DT) systems.  ...  OPTIMAL CONTROL AND GHJB EQUATION FOR NONLINEAR DT SYSTEMS Consider an affine in the control nonlinear DT dynamic system of the form (1) where , , , and .  ... 
doi:10.1109/tnn.2007.900227 pmid:18269941 fatcat:irka5ynl45aajf4cktx75hqssm

Wavelet neural network based controller design for non-affine nonlinear systems

Pramendra Kumar, Vikas Panwar
2020 Journal of Mathematics and Computer Science  
This paper addresses the design of wavelet neural network(WNN) based control scheme for non-affine nonlinear system with unknown control direction.  ...  Wavelet neural network is employed to approximate the uncertain part of control system. Since the learning capability of WNN is superior than any conventional NN for system identification.  ...  m ]; u, y ∈ R are the input and output of system (2.2); y,ÿ, . . . are the first and higher order derivative of y;u,ü, . . . are the first and higher order derivative of u; and f is the smooth unknown  ... 
doi:10.22436/jmcs.024.01.05 fatcat:axzlj2bnsvhh3haqjamqnl76ii

Active Disturbance Rejection Control for a Class of Non-affine Nonlinear Systems via Neural Networks

Wen-tao LIU, Tong ZHAO
2019 DEStech Transactions on Computer Science and Engineering  
An active disturbance rejection controller based on radial basis function (RBF) neural network is proposed for a class of non-affine nonlinear systems in this paper.  ...  It is proved that, the composite controller has faster response speed and higher tracking accuracy, which effectively improves the control performance of the system and alleviates the adverse effects caused  ...  Based on the approximation of RBFNN, the nonlinear inverse error and part of the filter can be expressed as Simulation Analysis In order to verify the effectiveness of the proposed scheme, we use MATLAB  ... 
doi:10.12783/dtcse/ica2019/30721 fatcat:idwrvrfa6zc4jcbhoihkvrxpoi

Reinforcement-Learning-Based Dual-Control Methodology for Complex Nonlinear Discrete-Time Systems With Application to Spark Engine EGR Operation

P. Shih, B.C. Kaul, S. Jagannathan, J.A. Drallmeier
2008 IEEE Transactions on Neural Networks  
systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances.  ...  A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear  ...  are unknown higher order terms.  ... 
doi:10.1109/tnn.2008.2000452 pmid:18701368 fatcat:k33cgcg4qvhxbbdarqk6kvby6m

Data-Driven Model Predictive Control using Interpolated Koopman Generators [article]

Sebastian Peitz and Samuel E. Otto and Clarence W. Rowley
2020 arXiv   pre-print
This way, control of nonlinear dynamical systems can be realized by means of switched systems techniques, using only a finite set of autonomous Koopman operator-based reduced models.  ...  This way, we combine the advantages of the data efficiency of approximating a finite set of autonomous systems with continuous controls.  ...  In many of these approaches, the Koopman operator is approximated for an augmented state (consisting of the actual state and the control) in order to deal with the non-autonomous control system.  ... 
arXiv:2003.07094v1 fatcat:xporncvksbf47gaui25zu3hbli

Integral Terminal Sliding Mode Control for a Class of Nonaffine Nonlinear Systems with Uncertainty

Qiang Zhang, Hongliang Yu, Xiaohong Wang
2013 Mathematical Problems in Engineering  
This paper is concerned with an integral terminal sliding mode tracking control for a class of uncertain nonaffine nonlinear systems.  ...  Firstly, the nonaffine nonlinear systems is approximated to facilitate the desired control design via a novel dynamic modeling technique.  ...  Acknowledgments This work was supported by Natural Science Foundation of Shandong Province under Grant ZR2012F Q030.  ... 
doi:10.1155/2013/636494 fatcat:wqagoo3n5jel3jq7ymu22hkjgm

Adaptive Neural Network Tracking Control for a Class of SISO Affine Nonlinear Uncertain Systems

Hui Hu, Peng Guo
2012 Journal of Computers  
A direct adaptive neural network tracking control scheme is presented for a class of SISO affine nonlinear uncertain systems. Uncertainties meet the match conditions.  ...  Parameters in neural networks are updated using a gradient descent method which designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the  ...  Moreover, nonlinearly parameterized approximators, such as multilayer neural network(MNN), can be linearized as linearly parameterized approximators, with the higher order terms of Taylor series expansions  ... 
doi:10.4304/jcp.7.5.1169-1175 fatcat:lty3ccb4brd6ffphd7mqohnmwm

ROBUST CONTROL OF END-TIDAL CO2 USING THE H∞ LOOP-SHAPING APPROACH

Anake Pomprapa, Berno Misgeld, Verónica Sorgato, André Stollenwerk, Marian Walter, Steffen Leonhardt
2013 Acta Polytechnica  
To control the carbon dioxide (CO 2 ) level effectively and automatically, system identification based on a human subject was performed using a linear affine model and a nonlinear Hammerstein structure  ...  For demonstration purposes, the closed-loop control ventilation system was successfully tested in a human volunteer.  ...  Acknowledgements The authors acknowledge financial support from the German Federal Ministry of Science and Education (Bundesministeriums für Bildung und Forschung -BMBF) within the Oxivent project under  ... 
doi:10.14311/ap.2013.53.0895 fatcat:jvnc7cna4rbdbekdxqmlra3pyy

Generalized Quadratic Linearization of Machine Models

Parvathy Ayalur Krishnamoorthy, Kamaraj Vijayarajan, Devanathan Rajagopalan
2011 Journal of Control Science and Engineering  
Also, solution of generalized quadratic linearization of a class of control affine systems is derived.  ...  But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system.  ...  But the approximate linearization, while removing nonlinearities up to a certain higher order, introduces nonlinearities into the system of higher order than those removed.  ... 
doi:10.1155/2011/926712 fatcat:sf3yokgdnneivdxzyktzmt3m4a

Recursive Analytic Solution of Nonlinear Optimal Regulators [article]

Nader Sadegh, Hassan Almubarak
2020 arXiv   pre-print
The paper develops an optimal regulator for a general class of multi-input affine nonlinear systems minimizing a nonlinear cost functional with infinite horizon.  ...  The resulting solution generates the optimal controller as a nonlinear function of the state vector up to a prescribed truncation order.  ...  In this paper, we solve the infinite horizon optimal control problem for nonlinear control affine systems.  ... 
arXiv:2006.15685v1 fatcat:r5wj4swoljdxjk7sovlgmxv3fe

Page 5086 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
Control 76 (2003), no. 5, 459-477. A general nonlinear system can be approximated with a finite set of linear affine systems.  ...  The domain of interest is divided into a finite number of polytopic regions. In each region, a linear system is used to approximate the nonlinear system.  ... 
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