scholarly journals The statistically invariant sets of controllable systems with random parameters

2011 ◽  
pp. 68-87 ◽  
Author(s):  
L.I. Rodina ◽  
Keyword(s):  
Invariant Sets ◽  
Random Parameters ◽  
Controllable Systems ◽  
Statistically Invariant Sets

Action-Minimizing Curves for Tonelli Lagrangians

2017 ◽  
Author(s):  
Alfonso Sorrentino
Keyword(s):  
Critical Value ◽  
The Other ◽  
Invariant Sets ◽  
Simple Pendulum ◽  
New Concepts ◽  
Peierls Barrier ◽  
Average Action

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical and symplectic properties, comparing them with the results obtained in the preceding chapter for the Mather sets. The relation between these new invariant sets and the Mather sets is described. As a by-product, the chapter introduces the Mañé's potential, Peierls' barrier, and Mañé's critical value. It discusses their properties thoroughly. In particular, it highlights how this critical value is related to the minimal average action and describes these new concepts in the case of the simple pendulum.

Simplified analysis of a stochastic system

1979 ◽  
Vol 44 (2) ◽  
pp. 328-339
Author(s):  
Vladimír Herles
Keyword(s):  
Statistical Analysis ◽  
Dynamic Behavior ◽  
Stochastic System ◽  
Additive Noise ◽  
Random Parameter ◽  
Systematic Difference ◽  
Order System ◽  
Constant Parameter ◽  
Random Parameters ◽  
Simplified Analysis

Contradictious results published by different authors about the dynamics of systems with random parameters have been examined. Statistical analysis of the simple 1st order system proves that the random parameter can cause a systematic difference in the dynamic behavior that cannot be (in general) described by the usual constant-parameter model with the additive noise at the output.

Transient response of the 1-st order dynamic system with fluctuating parameters

1979 ◽  
Vol 44 (7) ◽  
pp. 2184-2195
Author(s):  
Vladimír Herles ◽  
Jan Čermák ◽  
Antonín Havlíček
Keyword(s):  
Dynamic System ◽  
Dynamic Behavior ◽  
Transient Response ◽  
Flow Model ◽  
Stirred Tank ◽  
Order System ◽  
Random Parameters ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Theoretical Results

The paper deals with the analysis of the dynamic behavior of the 1st order system with two random parameters. The theoretical results have been compared with experiments on flow model of a stirred tank reactor.

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