scholarly journals A Unified Software Framework for Empirical Gramians

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Christian Himpe ◽  
Mario Ohlberger
Keyword(s):  
Nonlinear Systems ◽  
Dynamic System ◽  
Model Reduction ◽  
Linear Systems ◽  
Multiple Input Multiple Output ◽  
Computational Method ◽  
Software Framework ◽  
Balanced Truncation ◽  
Multiple Input ◽  
Input Multiple Output

A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical Gramians not only extended this concept to nonlinear systems but also provided a uniform computational method. This work introduces a unified software framework supplying routines for six types of empirical Gramians. The Gramian types will be discussed and applied in a model reduction framework for multiple-input multiple-output systems.

Adaptive finite-time neural backstepping control for multiple-input–multiple-output uncertain nonlinear systems with full state constraints

2021 ◽  
pp. 014233122198912
Author(s):  
Yan Wei ◽  
Pingfang Zhou ◽  
Yueying Wang ◽  
Dengping Duan ◽  
Jiwei Tang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Constraints ◽  
Multiple Input Multiple Output ◽  
Backstepping Control ◽  
Attitude Tracking ◽  
Multiple Input ◽  
Full State ◽  
Input Multiple Output ◽  
Full State Constraints

This paper investigates the issue of finite-time tracking control for multiple-input–multiple-output nonlinear systems subject to uncertainties and full state constraints. To deal with full state constraints directly, integral barrier Lyapunov functionals (iBLF) are introduced. By using finite-time stability theory, an iBLF-based adaptive finite-time neural control scheme is presented. To solve the problem of “explosion of complexity” in the design of traditional backstepping control, a new finite-time convergent differentiator is presented. Through stability analysis, all closed-loop signals are proved to be semi-globally uniformly ultimately bounded, the finite time convergence can be guaranteed, and the state constraints are never violated. Finally, the attitude tracking simulations for an autonomous airship are conducted to verify the effectiveness of the proposed scheme.

Model Independent Numerical Procedure for the Diagonalization of a Multiple Input Multiple Output Dynamic System

2011 ◽  
Vol 58 (4) ◽  
pp. 1588-1595 ◽  
Author(s):  
Gianluca Persichetti ◽  
Antonino Chiummo ◽  
Fausto Acernese ◽  
Fabrizio Barone ◽  
Rosario De Rosa ◽  
...  
Keyword(s):  
Dynamic System ◽  
Multiple Input Multiple Output ◽  
Numerical Procedure ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Model Independent
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