On the Nonlinear Observability of Polynomial Dynamical Systems

2021 ◽  
Vol 1 (1) ◽  
pp. 88-94
Author(s):  
Daniel Gerbet ◽  
Klaus Röbenack
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
State Space ◽  
Polynomial Dynamical Systems ◽  
Higher Dimensional ◽  
Dimensional State Space ◽  
System Properties ◽  
Controllability And Observability ◽  
Important System ◽  
Nonlinear Observability

Controllability and observability are important system properties in control theory. These properties cannot be easily checked for general nonlinear systems. This paper addresses the local and global observability as well as the decomposition with respect to observability of polynomial dynamical systems embedded in a higher-dimensional state-space. These criteria are applied on some example system.

Global Analysis of Nonlinear Time-Delayed Dynamical Systems

2011 ◽  
Author(s):  
Jian-Qiao Sun ◽  
Bo Song ◽  
Jie Yang
Keyword(s):  
Steady State ◽  
Dynamical Systems ◽  
State Space ◽  
Global Analysis ◽  
Stable Steady State ◽  
Domains Of Attraction ◽  
Infinite Dimensional ◽  
Dimensional State Space ◽  
Steady State Responses ◽  
State Responses

Time-delayed dynamical systems are defined in an infinite dimensional state-space. When the system has multiple stable steady-state responses, the global analysis of the system such as finding the domains of attraction and boundary basin has to be done in the infinite dimensional state-space. This paper examines this issue and shows that there are rich opportunities for global analysis research of nonlinear time-delayed dynamical systems.

scholarly journals Estimating Direction of Arrival by Using Two-Dimensional State-Space Balance Method

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Jun Wang ◽  
Hong Xiang ◽  
Shaoming Wei ◽  
Zhongsheng Sun
Keyword(s):  
State Space ◽  
Elevation Angle ◽  
Matrix Pencil ◽  
Direction Of Arrival ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Rectangular Array ◽  
Matrix Pencil Method ◽  
Dimensional State Space ◽  
Controllability And Observability

A study of a two-dimensional state-space balance (2D SSB) method for estimating direction of arrival (DOA) for uniform rectangular array (URA) is presented in this letter. The comprehensive utilization of controllability and observability matrices and automatic pairing technique are considered in this method by using the single snapshot. Therefore, the DOAs of elevation angle and azimuth angle can pair automatically and acquire better estimation performance compared with 2D matrix pencil method or unitary matrix pencil method. In addition, the proposed method can handle correlated signals directly without preprocessing. Simulation is conducted to verify the effectiveness of the proposed method.

Impact of control representations on efficiency of local nonholonomic motion planning

2011 ◽  
Vol 59 (2) ◽  
pp. 213-218 ◽  
Author(s):  
I. Duleba
Keyword(s):  
Motion Planning ◽  
State Space ◽  
Three Dimensional ◽  
Nonholonomic Systems ◽  
State Spaces ◽  
Controlled Systems ◽  
Higher Dimensional ◽  
Dimensional State Space ◽  
Optimal Motion Planning ◽  
Nonholonomic Motion Planning

Impact of control representations on efficiency of local nonholonomic motion planning In this paper various control representations selected from a family of harmonic controls were examined for the task of locally optimal motion planning of nonholonomic systems. To avoid dependence of results either on a particular system or a current point in a state space, considerations were carried out in a sub-space of a formal Lie algebra associated with a family of controlled systems. Analytical and simulation results are presented for two inputs and three dimensional state space and some hints for higher dimensional state spaces were given. Results of the paper are important for designers of motion planning algorithms not only to preserve controllability of the systems but also to optimize their motion.

scholarly journals Formal First Integrals of General Dynamical Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Jia Jiao ◽  
Wenlei Li ◽  
Qingjian Zhou
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Invariant Manifolds ◽  
First Integrals ◽  
Higher Dimensional ◽  
Complete Study ◽  
Planar Systems

The goal of this paper is trying to make a complete study on the integrability for general analytic nonlinear systems by first integrals. We will firstly give an exhaustive discussion on analytic planar systems. Then a class of higher dimensional systems with invariant manifolds will be considered; we will develop several criteria for existence of formal integrals and give some applications to illustrate our results at last.

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