Related Experiment Video
Updated: Oct 6, 2025
11:15
Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
Published on: June 27, 2013
33.9K
Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems
Xiafei Tang1, Yuyang Zhou2, Yiqun Zou3
1Engineering Research Center of the Ministry of Education (Power Grid Security Monitoring and Control Technology), Changsha University of Science and Technology, Changsha 410114, China.
Entropy (Basel, Switzerland)
|January 21, 2022
Summary
This study addresses randomness assignment in nonlinear systems using variance and entropy. A novel backstepping method transforms nonlinear systems into linear ones for analytical solutions, ensuring stability.
Area of Science:
- Control Theory
- Stochastic Systems
- Nonlinear Dynamics
Background:
- Continuous-time stochastic nonlinear systems present challenges due to non-Gaussian probability density functions.
- Variance and entropy are key metrics for characterizing system randomness.
Purpose of the Study:
- To investigate the randomness assignment problem for continuous-time stochastic nonlinear systems.
- To develop a method for analytically characterizing and assigning variance and entropy.
Main Methods:
- Formulation of system models using stochastic differential equations.
- Application of a novel backstepping-based design approach.
- Analytical solution using the Fokker-Planck-Kolmogorov equation.
Main Results:
- Conversion of stochastic nonlinear systems to linear stochastic processes.
- Analytical formulation of variance and entropy for system variables.
- Achievement of variance and entropy assignment through backstepping design parameters.
Conclusions:
- The proposed backstepping design scheme guarantees stability for randomness assignment.
- The method is effective for both single and multi-variate cases, validated by simulations.
Related Concept Videos
01:10Entropy Change in Reversible Processes
2.8K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.8K
01:20Entropy and the Second Law of Thermodynamics
3.3K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
3.3K
01:14The Second Law of Thermodynamics
5.9K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
5.9K
02:39Entropy
31.8K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
31.8K
01:31Classification of Systems-II
253
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
253
02:49Second Law of Thermodynamics
24.6K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic...
24.6K