scholarly journals A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems

2009 ◽  
pp. 427-457 ◽  
Author(s):  
F. Ammar Khodja ◽  
A. Benabdallah ◽  
C. Dupaix ◽  
M. González-Burgos
Keyword(s):  
Parabolic Systems ◽  
Time Dependent ◽  
Rank Condition ◽  
Kalman Rank Condition

scholarly journals A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems

2009 ◽  
Vol 9 (2) ◽  
pp. 267-291 ◽  
Author(s):  
Farid Ammar-Khodja ◽  
Assia Benabdallah ◽  
Cédric Dupaix ◽  
Manuel González-Burgos
Keyword(s):  
Parabolic Systems ◽  
Rank Condition ◽  
Kalman Rank Condition

Robustness and Controllability Analysis for Autonomous Navigation of Two-Wheeled Mobile Robots

2007 ◽  
Author(s):  
Alessio Salerno ◽  
Jorge Angeles
Keyword(s):  
Mobile Robots ◽  
Autonomous Navigation ◽  
Autonomous Robots ◽  
Upper Bounds ◽  
Small Time ◽  
Dynamics Model ◽  
Wheeled Mobile Robots ◽  
Rank Condition ◽  
Dynamics Response ◽  
Kalman Rank Condition

This work deals with the robustness and controllability analysis for autonomous navigation of two-wheeled mobile robots. The analysis of controllability of the systems at hand is conducted using both the Kalman rank condition for controllability and the Lie Algebra rank condition. We show that the robots targeted in this work can be controlled using a model for autonomous navigation by means of their dynamics model: kinematics will not be sufficient to completely control these underactuated systems. After having proven that these autonomous robots are small-time locally controllable from every equilibrium point and locally accessible from the remaining points, the uncertainty is modeled resorting to a multiplicative approach. The dynamics response of these robots is analyzed in the frequency domain. Upper bounds for the complex uncertainty are established.

scholarly journals Parabolic systems of Shilov-type with coefficients of bounded smoothness and nonnegative genus

2017 ◽  
Vol 9 (1) ◽  
pp. 72-85
Author(s):  
V.A. Litovchenko ◽  
G.M. Unguryan
Keyword(s):  
Cauchy Problem ◽  
Space Variable ◽  
Parabolic Systems ◽  
Type Systems ◽  
Variable Coefficients ◽  
Time Dependent ◽  
Modern Theory ◽  
New Class ◽  
The Cauchy Problem ◽  
Derivatives Of

The Shilov-type parabolic systems are parabolically stable systems for changing its coefficients unlike of parabolic systems by Petrovskii. That's why the modern theory of the Cauchy problem for class by Shilov-type systems is developing abreast how the theory of the systems with constant or time-dependent coefficients alone. Building the theory of the Cauchy problem for systems with variable coefficients is actually today. A new class of linear parabolic systems with partial derivatives to the first order by the time $t$ with variable coefficients that includes a class of the Shilov-type systems with time-dependent coefficients and non-negative genus is considered in this work. A main part of differential expression concerning space variable $x$ of each such system is parabolic (by Shilov) expression. Coefficients of this expression are time-dependent, but coefficients of a group of younger members may depend also a space variable. We built the fundamental solution of the Cauchy problem for systems from this class by the method of sequential approximations. Conditions of  minimal smoothness on  coefficients of the systems by  variable $x$ are founded, the smoothness of solution is investigated and estimates of derivatives of this solution are obtained.  These results are important for  investigating  of the correct solution of the Cauchy problem for this systems in different functional spaces, obtaining forms of description of the solution of this problem and its properties.

scholarly journals STABILITY AND CONTROLABILITY ANALYSIS ON LINEARIZED DYNAMIC SYSTEM EQUATION OF MOTION OF LSU 05-NG USING KALMAN RANK CONDITION METHOD

2020 ◽  
Vol 18 (2) ◽  
pp. 81
Author(s):  
Angga Septiyana
Keyword(s):  
Dynamic System ◽  
State Space ◽  
Equations Of Motion ◽  
Moment Equation ◽  
Equation Of Motion ◽  
Stability Control ◽  
Rank Condition ◽  
System Equation ◽  
Kalman Rank Condition ◽  
Scientific Platform

This paper discusses the stability, control and observation of the dynamic system of the Lapan Surveillance UAV 05-NG (LSU 05-NG) aircraft equation. This analysis is important to determine the performance of aircraft when carrying out missions such as photography, surveillance, observation and as a scientific platform to test communication based on satellite. Before analyzing the dynamic system, first arranged equations of motion of the plane which includes the force equation, moment equation and kinematics equation. The equation of motion of the aircraft obtained by the equation of motion of the longitudinal and lateral directional dimensions. Each of these equations of motion will be linearized to obtain state space conditions. In this state space, A, B and C is linear matrices will be obtained in the time domain. The results of the analysis of matrices A, B and C show that the dynamic system in the LSU 05-NG motion equation is a stable system on the longitudinal dimension but on the lateral dimension directional on the unstable spiral mode. As for the analysis of the control of both the longitudinal and lateral directional dimensions, the results show that the system is controlled.

Sign in / Sign up

Export Citation Format

Share Document