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Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Raquel S. Rodríguez, Gilberto Gonzalez Avalos, Noe Barrera Gallegos, Gerardo Ayala-Jaimes, Aaron Padilla Garcia
2021 Symmetry  
This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization.  ...  Hence, a first step can be to linearize this nonlinear system on an operation point.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym13050854 fatcat:4oxzpfvbmzaj3cdlknwf42ydjy

On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models

Sen
2019 Entropy  
dynamics with respect to a given reference nominal one and, eventually, an unknown structured nonlinear dynamics.  ...  This paper formulates the properties of point reachability and approximate point reachability of either a targeted state or output values in a general dynamic system which possess a linear time-varying  ...  , of either a targeted state or targeted output value in a dynamic system which has a linear time-varying dynamics with respect to a given nominal one and an unknown structured nonlinear dynamics with  ... 
doi:10.3390/e21111045 fatcat:xts47fojcbdlvpfo6wphrvgr5i

Block-Oriented Identification Using The Best Linear Approximation: Benefits And Drawbacks

Maarten Schoukens
2017 Zenodo  
One class of these approaches uses the so-called best linear approximation to initialize the identification algorithm.  ...  This paper gives an overview of the benefits and drawbacks of using identification algorithms based on the best linear approximation.  ...  This paper considers the Best Linear Approximation (BLA) framework [6] , [7] to estimate a linear approximation of a nonlinear system..  ... 
doi:10.5281/zenodo.291905 fatcat:jbtjvsksdvae5ozbakqxt6i2su

2020 Index IEEE Transactions on Automatic Control Vol. 65

2020 IEEE Transactions on Automatic Control  
., +, TAC Jan. 2020 412-418 Nonlinearity Estimator-Based Control of A Class of Uncertain Nonlinear Systems.  ...  ., +, TAC Oct. 2020 4016- 4030 Nonlinearity Estimator-Based Control of A Class of Uncertain Nonlinear Systems.  ...  Linear programming A Decentralized Event-Based Approach for Robust Model Predictive Control.  ... 
doi:10.1109/tac.2020.3046985 fatcat:hfiqhyr7sffqtewdmcwzsrugva

A Review of Fuzzy Logic and Neural Network Based Intelligent Control Design for Discrete-Time Systems

Yiming Jiang, Chenguang Yang, Hongbin Ma
2016 Discrete Dynamics in Nature and Society  
This survey aims to present a summary of the state of the art of the design of FLC and NN-based intelligent control for discrete-time systems.  ...  The rapid development of digital computer based control systems requires control signals to be calculated in a digital or discrete-time form.  ...  ADP is a reinforcement learning method to give solution to the dynamic programming utilizing function approximating the value function based on adaptive approach [97] . P.  ... 
doi:10.1155/2016/7217364 fatcat:qkjxrfnvpja4zjzk2cgmg6x7tm

Identification of block-oriented nonlinear systems starting from linear approximations: A survey

Maarten Schoukens, Koen Tiels
2017 Automatica  
One class of these approaches uses linear approximations to initialize the identification algorithm.  ...  Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use.  ...  through the Inter university Poles of Attraction IAP VII/19 DYSCO program, and the ERC advanced grant SNLSID, under contract 320378.  ... 
doi:10.1016/j.automatica.2017.06.044 fatcat:xkezwanxmrfd5ehky4xcvcqssm

Scanning the issue

2004 IEEE Transactions on Automatic Control  
Such systems can also be seen as a sort of differential inclusion, or (in special cases) as linear complementarity systems, which in turn are a class of hybrid dynamical systems.  ...  The multibody systems are defined on a trivial principal fiber bundle by a Lagrangian that characterizes the base body motion and shape dynamics.  ...  Such systems can also be seen as a sort of differential inclusion, or (in special cases) as linear complementarity systems, which in turn are a class of hybrid dynamical systems.  ... 
doi:10.1109/tac.2004.825606 fatcat:ajdh4qagszhhpgu4qgxjvjw25u

Survey of gain-scheduling analysis and design

D. J. Leith, W. E. Leithead
2000 International Journal of Control  
The main theoretical results which, for a broad class of nonlinear systems, relate the dynamic characteristics of a member of the class to those of an associated family of linear systems are reviewed in  ...  The theoretical results relating the dynamic characteristics of a nonlinear system to those of a family of linear systems are reviewed in section 2.  ...  Implement a nonlinear controller based on the family of linear controllers, (15)-(17).  ... 
doi:10.1080/002071700411304 fatcat:oxv67zumpjecliasoaewuoeivm

Neural network-based control design: an LMI approach

S. Limanond, J. Si
1998 IEEE Transactions on Neural Networks  
A linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a statefeedback control law for the nonlinear system based on the  ...  Our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin.  ...  ACKNOWLEDGMENT The authors are thankful to D. Banjerdpongchai at Stanford University for the discussions on LMI.  ... 
doi:10.1109/72.728392 pmid:18255820 fatcat:xpo4ozhdjvf5rmzykfwwwcflua

Neural network-based control design: an LMI approach

S. Limanond, J. Si
1998 Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)  
A linear difference inclusion representation is then established for this class of approximating neural networks and is used to design a statefeedback control law for the nonlinear system based on the  ...  Our design approach is to approximate the nonlinear system with a multilayer perceptron of which the activation functions are of the sigmoid type symmetric to the origin.  ...  ACKNOWLEDGMENT The authors are thankful to D. Banjerdpongchai at Stanford University for the discussions on LMI.  ... 
doi:10.1109/acc.1998.703553 fatcat:q5lgytwztjaubeh2r3naewwglq

2007 Index IEEE Transactions on Automatic Control Vol. 52

2007 IEEE Transactions on Automatic Control  
., H Control and Estimation of Retarded State-Multiplicative Stochastic Systems; TAC Sept. 1773Sept.  ...  ., Approximation Metrics for Discrete and Continuous Systems; TAC May 2007 782-798 Giua, A., see Basile, F., TAC Feb. 2007 306-311 Giua, A., Seatzu, C., and Corona, C., Oct. 2007 Oct.  ...  ., +, TAC March 2007 442-453 Nonlinear filters Closed-Loop Behavior of a Class of Nonlinear Systems Under EKF-Based Control. Ahrens, J.  ... 
doi:10.1109/tac.2007.913948 fatcat:vpztpth7jnhk7b5o5bt2nyrrdm

Application of non-linear control to a magnetic levitation system

Rafael Antonio Acosta Rodriguez, Octavio Jose Salcedo Parra, Giovanny Mauricio Tarazona Bermudez
2017 International Journal of Mathematical Analysis  
This paper evaluates the nonlinear control applied to a magnetic levitating plant, it is explained in detail the nonlinear model of the plant, the state variables, perturbation vector.  ...  A state feedback control was triggered by applying a state observer. Finally it was modeled under the control law found in the presence of disturbances.  ...  Background This study presents a focus on adaptive decentralized dynamic surface (DSC) control for a large scale class, at the same time a nonlinear system with unknown nonlinear functions, unknown control  ... 
doi:10.12988/ijma.2017.710137 fatcat:37neqq7pnjai3lpwylhc4sgzay

Mathematical Modeling, Analysis, and Control of Hybrid Dynamical Systems

Peng Shi, Hamid Reza Karimi, Rongni Yang, Xiaojie Su
2013 Mathematical Problems in Engineering  
Margret obtains an upper bound for the distance from a controllable switched linear system to a set of uncontrollable ones.  ...  He et al. presents the solution of the output tracking problem for a class of nonlinear affine systems.  ...  Acknowledgments We would like to express our great appreciation to the authors for their remarkable contributions in assisting us.  ... 
doi:10.1155/2013/820948 fatcat:hjyoxv23rna6dmuwhr2sx2fceu

Page 6290 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
The authors review the design of a stabilizing and regulation con- trol law based on sliding mode techniques for a class of nonlinear singularly perturbed systems.  ...  Summary: “The problem under consideration is to obtain a canon- ical decomposition of nonlinear dynamic systems. This decompo- sition generalizes a well-known decomposition in the linear case.  ... 

Page 5814 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
The first scheme is based on input-output linearization of the system. An adaptive version of the algorithm from a paper by J. Descusse and C. H.  ...  Systems Sci. 24 (1993), no. 4, 777-788. Summary: “This article proposes a new state approximation tech- nique for a class of nonlinear observable systems.  ... 
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