Controllability Gramian and Kalman rank condition for mean-field control systems

This paper is concerned with the exact controllability of linear mean-field stochastic systems with deterministic coefficients. With the help of the theory of mean-field backward stochastic differential equations (MF-BSDEs, for short) and some delicate analysis, we obtain a mean-field version of the Gramian matrix criterion for the general time-variant case, and a mean-field version of the Kalman rank condition for the special time-invariant case.

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

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.

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

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.