Comments on ‘ Dynamic feedback methodology for interconnected control systems ’ and ‘ Dynamic multilevel optimization for a class of non-linear systems ’

1981 ◽  
Vol 34 (5) ◽  
pp. 1039-1043 ◽  
Author(s):  
JUHANI HIRVONEN
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Dynamic Feedback ◽  
Multilevel Optimization ◽  
Non Linear ◽  
Non Linear Systems

scholarly journals Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2092
Author(s):  
Simone Fiori
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Linear Control Systems ◽  
First Order ◽  
Curved Manifolds ◽  
Non Linear ◽  
Covariant Derivation ◽  
Non Linear Systems ◽  
And Control

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

scholarly journals Control systems with time lags

1976 ◽  
Vol 19 (4) ◽  
pp. 478-492 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Time Lags ◽  
Optimal Controls ◽  
State Variables ◽  
Delayed Effects ◽  
Non Linear ◽  
Non Linear Systems

AbstractNecessary conditions for optimal controls are given for non-linear systems with time delayed effects in both control and state variables.

scholarly journals Identification of Non-linear Systems through Convolutional Neural Network

2019 ◽  
Vol 8 (3) ◽  
pp. 3429-3434
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Convolutional Neural Network ◽  
Control Systems ◽  
Linear Systems ◽  
Test Data ◽  
Training Data ◽  
Analysis And Design ◽  
Non Linear ◽  
Non Linear Systems

The theory of control systems deals with the analysis and design of interacting components of a system in a configuration that provides the desired behavior. This paper deals with the problem of the identification of non-linear systems through Convolutional Neural Network (CNN). We propose a structure of a CNN and perform simulations with test data using unsupervised learning for the identification of nonlinear systems. Also, MLP is used to compare the results when there is noise in the training data, which allows us to see that the proposed CNN has better performance and can be used for cases where the noise is present. The proposed CNN is validated with test data. Tests are carried out with Gas oven data, comparing the proposed structure of CNN with a MLP. When there is noise in the data, CNN has better performance than MLP.

scholarly journals A linear dynamic feedback controller for non-linear systems described by matrix differential equations of the second and first orders

2019 ◽  
Vol 52 (7-8) ◽  
pp. 913-921 ◽  
Author(s):  
Paweł Skruch ◽  
Marek Długosz
Keyword(s):  
Differential Equations ◽  
Linear Systems ◽  
Differential Algebraic Equations ◽  
Feedback Controller ◽  
Dynamic Feedback ◽  
Algebraic Equations ◽  
Linear Dynamic ◽  
Wide Range ◽  
Non Linear ◽  
Non Linear Systems

The paper presents a design scheme of the linear dynamic feedback controller for some non-linear systems. These systems are mathematically described by matrix non-linear differential equations of the first and second orders. A first-order form of the studied systems includes some types of differential-algebraic equations. The stability property of the non-linear systems with the linear controller is assured by an appropriate definition of the system output, and the linear dynamic compensator is an important part of the feedback control system. The order of the dynamic part is equal to the size of the system input and is independent of the size of the system state vector. The asymptotic stability in the Lyapunov sense is analysed and proved by the use of Lyapunov functionals and LaSalle’s invariance principle. Stabilisation in a wide range of controller parameters improves the system’s robustness.

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

Distributed track‐to‐track fusion for non‐linear systems with Gaussian mixture noise

2019 ◽  
Vol 13 (5) ◽  
pp. 740-749 ◽  
Author(s):  
Kelin Lu ◽  
Changyin Sun ◽  
Qien Fu ◽  
Qian Zhu
Keyword(s):  
Linear Systems ◽  
Gaussian Mixture ◽  
Track Fusion ◽  
Non Linear ◽  
Non Linear Systems
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