A simpler and elegant algorithm for computing fractal dimension in higher dimensional state space

Pramana ◽  
2000 ◽  
Vol 54 (2) ◽  
pp. L331-L336 ◽  
Author(s):  
S Ghorui ◽  
A K Das ◽  
N Venkatramani
Keyword(s):  
Fractal Dimension ◽  
State Space ◽  
Higher Dimensional ◽  
Dimensional State Space

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.

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 A construction of the general relativistic Boltzmann equation

1984 ◽  
Vol 7 (3) ◽  
pp. 591-597 ◽  
Author(s):  
P. Dolan ◽  
A. C. Zenios
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Simple Model ◽  
State Space ◽  
Differential Forms ◽  
Relativistic Boltzmann Equation ◽  
Dimensional State Space ◽  
General Relativistic ◽  
Invariant Differential

Our work depends essentially on the notion of a one-particle seven-dimensional state-space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state-space.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

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