scholarly journals Acceleration of implicit schemes for large linear systems of differential–algebraic equations

2020 ◽  
pp. 113364
Author(s):  
Mouhamad Al Sayed Ali ◽  
Miloud Sadkane
Keyword(s):  
Linear Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Implicit Schemes ◽  
Large Linear Systems

Control Constraint Realization for Multibody Systems

2009 ◽  
Author(s):  
Alessandro Fumagalli ◽  
Pierangelo Masarati ◽  
Marco Morandini ◽  
Paolo Mantegazza
Keyword(s):  
Linear Systems ◽  
Multibody Systems ◽  
Matrix Pencil ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Control Constraint ◽  
Practical Observation ◽  
Alternative Condition ◽  
Deformable Bodies

This paper discusses the problem of control constraint realization applied to generic under-actuated multibody systems. The conditions for the realization are presented. Focus is placed on the tangent realization of the control constraint. An alternative condition is formulated, based on the practical observation that Differential-Algebraic Equations (DAE) need to be integrated using implicit algorithms, thus naturally leading to the solution of the problem in form of matrix pencil. The analogy with the representation of linear systems in Laplace’s domain is also discussed. The formulation is applied to the solution of simple, yet illustrative problems, related to rigid and deformable bodies. Some implications of considering deformable continua are addressed.

scholarly journals Convergence theory of iterative methods based on proper splittings and proper multisplittings for rectangular linear systems

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1835-1851
Author(s):  
Vaibhav Shekhar ◽  
Chinmay Giri ◽  
Debasisha Mishra
Keyword(s):  
Linear Systems ◽  
Iterative Scheme ◽  
Iterative Solution ◽  
Differential Algebraic Equations ◽  
Convergence Theory ◽  
Algebraic Equations ◽  
Linear System Of Equations ◽  
Convergence Results ◽  
Comparison Results ◽  
Singular Linear System

Multisplitting methods are useful to solve differential-algebraic equations. In this connection, we discuss the theory of matrix splittings and multisplittings, which can be used for finding the iterative solution of a large class of rectangular (singular) linear system of equations of the form Ax = b. In this direction, many convergence results are proposed for different subclasses of proper splittings in the literature. But, in some practical cases, the convergence speed of the iterative scheme is very slow. To overcome this issue, several comparison results are obtained for different subclasses of proper splittings. This paper also presents a few such results. However, this idea fails to accelerate the speed of the iterative scheme in finding the iterative solution. In this regard, Climent and Perea [J. Comput. Appl. Math. 158 (2003), 43-48: MR2013603] introduced the notion of proper multisplittings to solve the system Ax = b on parallel and vector machines, and established convergence theory for a subclass of proper multisplittings. With the aim to extend the convergence theory of proper multisplittings, this paper further adds a few results. Some of the results obtained in this paper are even new for the iterative theory of nonsingular linear systems.

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.

Control Constraint Realization for Multibody Systems

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Alessandro Fumagalli ◽  
Pierangelo Masarati ◽  
Marco Morandini ◽  
Paolo Mantegazza
Keyword(s):  
Linear Systems ◽  
Multibody Systems ◽  
Matrix Pencil ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Control Constraint ◽  
Practical Observation ◽  
Alternative Condition ◽  
Deformable Bodies

This paper discusses the problem of control constraint realization applied to generic underactuated multibody systems. The conditions for the realization are presented. Focus is placed on the tangent realization of the control constraint. An alternative condition is formulated, based on the practical observation that differential-algebraic equations need to be integrated using implicit algorithms, thus naturally leading to the solution of the problem in form of matrix pencil. The analogy with the representation of linear systems in Laplace’s domain is also discussed. The formulation is applied to the solution of simple, yet illustrative problems, related to rigid and deformable bodies. Some implications of considering deformable continua are addressed.

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